Graph the polynomial function f(x) = x^3 + 3x^2 – 4x – 12 using its intercepts and end behavior

The end behavior of the function is as x → -∞, f(x) → -∞ and s x → +∞, f(x) → +∞.

The nature of the value when the function parameter gets closer to +∞ and - ∞ is the end behavior of a function. The term with the highest degree determines how a polynomial function will behave in the end.

Look at the polynomial function's leading term to identify its final behavior. The leading term will dominate the graph because it has the highest power and will therefore grow much more quickly than the other terms as x gets very large or very small.

The given function is f(x) = 7x⁷ + 12x⁵ - 6x³ + 2x - 18

Graph the function. From the graph, the end behavior of the function is given as

As x → -∞, f(x) → -∞

As x → +∞, f(x) → +∞

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Answer:

Step-by-step explanation: 6^4 would be 1296 because its 6 times 6 times 6 times 6. Then 6 times 6 times 6 times 6 times 6 times 6 times 6 times 6 would be 1,679,616. 6 times 6 times 6 would be 216. 1,679,616/216 would be 7776. 1296 times 7776 is 10,077,696.

Hoped This Helped!

The probability of purchasing mineral rights to exactly one of the two mountains is 0.51.

Probability turned into added into arithmetic to are expecting the possibility of an occasion occurring. Probability essentially approach how in all likelihood it's miles that some thing will happen. This is the fundamental principle of possibility and is likewise utilized in possibility distributions to examine feasible consequences of random experiments.

Given information:

A company is considering purchasing materials:

The probability of purchasing mineral rights

Form the first mountain P1 = 0.55

From the second mountain P2 = 0.4

As the decision is made independently

So, P(P2∩ notP1) = 0.55 * 0.6

P(P2∩ notP1) = 0.33

Similarly, the value of

P(P2∩ notP1) =0.4 * 0.45

P(P2∩ notP1) = 0.15

Hence ,

P = 0.33 + 0.18

P = 0.51

Hence , the probability of purchasing mineral rights to exactly one of the two mountains is 0.51.

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Answer:

1,750m

Step-by-step explanation:

3x9x10x5 = 1,750

Using the given model, we can complete the expression

                       12 + 16 = 4 × (4 + 3).

What are the area of a rectangle and a square?

The area of a rectangle having length "l" and breadth "b" is

                 Area of a Rectangle = l × b.

The area of a square with side "a",

                 Area of a square = side².

Let the given expression be 12 + 16 =  x × (y + x)

For the given figure the area of the square which is displayed in pink portion can be expressed as

                   Area = y²

                      16 = y²

Taking square root on both sides, we get

                      y = 4.

Now for the red part, we get the length of the rectangle i.e., y = 4.

                   Area of a rectangle = length * breadth

                                            12 = 4 * x

                                             x = 3.

Hence, the expression would look like

                        12 + 16 = 4 × (4 + 3)

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Answer:

True, True, False, True

Step-by-step explanation:

For line 2:

[tex]0 + 5(2) = 10[/tex]

[tex]0 + 10 = 10[/tex]

True

-2x - 2y = 4-------> -x - y = 2

x + 5y = 10-----> x + 5y = 10

--------------

4y = 12

y = 3, x = -5

(-5, 3) is a solution to the system----True

(4, 10) is a solution to the system----False

For Line 1:

[tex] - 2( - 10) - 2(8) = 4[/tex]

[tex]20 - 16 = 4[/tex]

True

The proportion statement is 2/3. The missing angles are CK = 12, GN = 15 and GT = 9

Given that: Polygon ROCK ~  Polygon GNAT.

The symbol ~ means the polygons are similar to each other. That means the ratios of all their corresponding sides are the same. Thus:

CO/AN = 4/6 = 2/3 (This is the proportion statement)

We can also say CK/AT= 2/3 because the ratios of all their corresponding sides are the same

With this, we can determine  the missing sides:

CK/AT= 2/3     where AT = 18

CK/18= 2/3

CK = (18×2)/3 = 12

OR/GN = 2/3    where OR = 10

10/GN = 2/3

2GN = 10×3

2GN = 30

GN = 30/2 = 15

KR/GT = 2/3   where KR = 6

6/GT = 2/3

2GT = 6×3

2GT = 18

GT = 18/2 = 9

Therefore, the proportion statement is 2/3, and the missing angles are CK = 12, GN = 15 and GT = 9

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The domain of the first function is {-2,0,2,4} and range is {-3,-1,0} and the domain of second function is {-3,-1,0,3,3} and the range is {-1,0,1,2,3}.

The domain of a function is the set of values that we are allowed to plug into function. This set is the x- values in a function. The range of a function is the set of values that the function assumes. This set is the values that the function shoots out after we plug an x-value in.

The domain is the x- value of the function and as we can see the mapping on the top left is assigned as x, hence the value of x is {-2,0,2,4} and the range is the y value of the function, as assigned {-3,-1,0}.

In the graph below, the domain is {-3,-1,0,3,3} as it is the x- values and the range is y value of the point given as {-1,0,1,2,3}.

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Answer:

x=14

y=2

Step-by-step explanation:

a: to do this we isolate x

x-2=6y

 +2.  +2

x=6y+2

b now substitute it into an equation

6y+2-2y=10

4y+2=10

    -2. -2

4y=8

/4. /4

y=2

now fill in y to find x

x-2(2)=10

x-4=10

 +4. +4

x=14

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Answer:

simplify the equation

5x+3x

4+2

8x+6

The answer will be 8x+6

Answer:

1.786

Step-by-step explanation:

(A) stamped envelope will cost 5+s pence

6 stamped envelopes will cost 6(5+s) pence

n stamped envelopes will cost n(5+s) pence

(B) expanded form of the ii part is 30+6s pence

and expanded form of the iii part is 5n+ns pence

As an envelope cost 5 pence and stamp cost s pence

(I) to get an stamped envelope we need to buy an envelope and the we have to get a stamp so the collective sum will be the cost that is

5+s pence

(II)to get 6 stamped envelope we need to buy 6 envelopes and the we have to get 6 stamps so the collective sum will be the cost that is

6(5+s) pence

(III))to get n stamped envelope we need to buy n envelopes and the we have to get n stamps so the collective sum will be the cost that is

n(5+s) pence

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Answer:

x = 45 Yes

Step-by-step explanation:

x+3x+2x+90= 360°

6x= 270

x=45

A= 2x = 90°

so yes both A and B makes 90° so they should be parallel

The required measure of m∠BVC is 90 degrees in the given figure.

A parallelogram is defined as a special type of quadrilateral that has both pairs of opposite sides parallel and equal.

A parallelogram is a square and a rhombus is a square.

We have been given a figure which shows a rhombus as a parallelogram

The adjacent sides of a parallelogram must be equal, and the angles formed by the four sides must be 90 degrees for a rhombus to be a square.

According to the given figure,

This represents m∠BVC = 90°

Therefore, the required measure of m∠BVC is 90 degrees.

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Answer:

y-intercept b = 2

Step-by-step explanation:

y-intercept is the point where the line intersects the y-axis.so, at y-intercept the x-coordinate is 0.

    In this graph the line intersects the y-axis at (0,2).

So, y -intercept b = 2

[tex]\frac{3}{4} +\frac{1}{6} =\frac{18}{24} +\frac{4}{24} =\frac{22}{24}[/tex]

but 22/24 can be reduced to:

[tex]\frac{22}{24} =\frac{11}{12}[/tex]

Only set (B) represents the side lengths of a right triangle.

In right triangle,

[tex](Hypotenuse)^{2} = (Perpendicular)^{2}+(Base)^{2}[/tex]

(A) [tex]8^{2} = 16[/tex]

     [tex]12^{2} = 144[/tex]

     [tex]15^{2} = 225[/tex]

    225 ≠ 144 + 16

(B) [tex]10^{2} = 100[/tex]

     [tex]24^{2} = 576[/tex]

     [tex]26^{2} = 676[/tex]

    676 = 576 + 100

(C) [tex]12^{2} = 144[/tex]

     [tex]20^{2} = 400[/tex]

     [tex]25^{2} = 625[/tex]

    625 ≠ 400 + 144

(D) [tex]15^{2} = 225[/tex]

     [tex]18^{2} = 324[/tex]

     [tex]20^{2} = 400[/tex]

    400 ≠ 324 + 225

Only (B) satisfies the condition.

Correct question,

Which set of numbers can represent the side lengths, in centimeters, of a right triangle?

(A) 8, 12, 15  (B) 10, 24, 26  (C) 12, 20, 25  (D) 15, 18, 20.

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[tex]\sqrt[3]{-8x^{24}y^{36}} = \sqrt[3]{-8}\cdot \sqrt[3]{x^{24}}\cdot \sqrt[3]{y^{36}}[/tex]

[tex]\sqrt[3]{8}=-2[/tex]   because [tex](-2)(-2)(-2)= -8[/tex]

[tex]\sqrt[3]{x^{24}}=x^8[/tex]   because [tex](x^8)(x^8)(x^8)=x^{24}[/tex]

[tex]\sqrt[3]{y^{36}}=y^{12}[/tex]   because [tex](y^{12})(y^{12})(y^{12})=y^{36}[/tex]

Therefore [tex]\sqrt[3]{-8x^{24}y^{36}} = -2x^8y^{12}[/tex]

Answer:

[tex]-2x^8y^{12}[/tex]

Step-by-step explanation:

Given expression:

[tex]\sqrt[3]{-8x^{24}y^{36}}[/tex]

[tex]\textsf{Apply radical rule} \quad \sqrt[n]{ab}=\sqrt[n]{a}\sqrt[n]{b}:[/tex]

[tex]\implies \sqrt[3]{-8}\sqrt[3]{x^{24}}\sqrt[3]{y^{36}}[/tex]

[tex]\textsf{Apply exponent rule} \quad \sqrt[n]{a}=a^{\frac{1}{n}}:[/tex]

[tex]\implies \left(-8\right)^{\frac{1}{3}}\left(x^{24}\right)^{\frac{1}{3}}\left(y^{36}\right)^{\frac{1}{3}}[/tex]

Rewrite 8 as 2³:

[tex]\implies \left(-2^3\right)^{\frac{1}{3}}\left(x^{24}\right)^{\frac{1}{3}}\left(y^{36}\right)^{\frac{1}{3}}[/tex]

[tex]\textsf{Apply exponent rule} \quad (a^b)^c=a^{bc}:[/tex]

[tex]\implies -2^{\frac{3}{3}}x^{\frac{24}{3}}y^{\frac{36}{3}}[/tex]

Simplify:

[tex]\implies -2x^8y^{12}[/tex]

Answer: A change from 20 to 22 represents a positive change (increase) of 10% Use the formula found below on this webpage to find the percent change by replacing the given values: Percent change = New - Old|Old| × 100% Percent change = 22 - 20 |20| × 100% = 2 20 × 100 = 10% (increase)

Answer: 10%

How: you know that 10 percent of 20 is 2 because you divide it by 10. by this you'll know that you are adding an extra 10 percent onto 20 to make it 22.

Answer:

The perimeter of [tex]\triangle[/tex][tex]PQR[/tex] is [tex]16[/tex] feet

Step-by-step explanation:

The perimeter of [tex]\triangle PQR[/tex] can be calculated as follows

Since [tex]\overline{PQ} \cong \overline{PR}[/tex] , then the length of [tex]PQ[/tex] is equal to the length of [tex]PR[/tex]

[tex]PQ = PR = 5~\text{feet}[/tex]

Since the angle [tex]\angle PSR[/tex] is [tex]90^{\circ}[/tex], then [tex]\triangle PSR[/tex] is a right triangle

Since [tex]\triangle PSR[/tex] is a right triangle, then the length of [tex]RS[/tex] can be calculated by the Pythagorean theorem as follows

[tex]c^{2}=a^{2}+b^{2}[/tex]

Where [tex]c[/tex] is the hypotenuse or the side [tex]PR[/tex], [tex]a[/tex] is the side [tex]RS[/tex], and [tex]b[/tex] is the side [tex]PS[/tex]

Substitute [tex]5[/tex] for [tex]PR[/tex], [tex]4[/tex] for [tex]PS[/tex] into the Pythagorean theorem

[tex]5^{2}=a^{2}+4^{2}[/tex]

Simplify the equation

[tex]25=a^{2}+16[/tex]

Move [tex]16[/tex] from the right side to the left side and change its sign to negative

[tex]25-16=a^{2}[/tex]

Simplify the equation

[tex]9 = a^{2}[/tex]

Find the value of [tex]a[/tex] by taking square root of both sides of the equation

[tex]\sqrt{9}=\sqrt{a^{2}}[/tex]

[tex]3 = a[/tex]

As a matter of fact the square root of [tex]9[/tex] are [tex]3[/tex] and [tex]-3[/tex], but disregard the negative value since the length value is never negative

Since the value of [tex]a[/tex] is [tex]3[/tex], then the length of [tex]RS[/tex] is [tex]3[/tex] feet

Since the angle [tex]\angle PSR[/tex] is [tex]90^{\circ}[/tex], then angle [tex]\angle PSQ[/tex] is also [tex]90^{\circ}[/tex] or

[tex]\angle PSQ = \text{straight angle}-90^{\circ}[/tex]

[tex]\angle PSQ = 180^{\circ}-90^{\circ}=90^{\circ}[/tex]

Since [tex]\overline{PQ} \cong \overline{PR}[/tex]  and [tex]\angle PSQ = \angle PSR[/tex], then [tex]\triangle PSR \cong \triangle PSQ[/tex]

Since [tex]\triangle PSR \cong \triangle PSQ[/tex], then the length of [tex]RS[/tex] is equal to the length of [tex]QS[/tex]

[tex]RS=QS=3~\text{feet}[/tex]

The perimeter of [tex]\triangle PQR[/tex] is the sum of the length of the following sides

[tex]\text{the perimeter of} ~\triangle PQR= PQ+QS+RS+PR[/tex]

Substitute [tex]5[/tex] for [tex]PQ[/tex], [tex]3[/tex] for [tex]QS[/tex], [tex]3[/tex] for [tex]RS[/tex], [tex]5[/tex] for [tex]PR[/tex] in the expression of the perimeter

[tex]\text{the perimeter of} ~\triangle PQR= 5+3+3+5[/tex]

Simplify the equation

[tex]\text{the perimeter of} ~\triangle PQR=16~\text{feet}[/tex]

Hence the perimeter of [tex]\triangle{PQR}[/tex] is [tex]16~\text{feet}[/tex]

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120 pints of first mixture and 20 pints of second mixture need to make 140 pints new mixture that 70% pure fruit juice.

Let we have to mix existing mixture in x,y respectively in amount to make the new mix of 70% purity.

Given that the first type is 65% pure.

So the pure juice = 65x/100

Given the second type is 100% pure.

So amount of pure juice in it = 100y/100

So the amount of pure juice in new mix = 65x/100+100y/100 = (65x+100y)/100

So the total amount of new mix = x+y

According to question,

((65x+100y)/100)/(x+y) = 70/100

(13x+20y)/(20x+20y) = 7/10

(13x+20y)/(2x+2y) = 7

13x+20y = 14x+14y

14x-13x = 20y-14y

x = 6y

x:y = 6:1

So we have to mix the existing mixture in 6:1 ratio.

So to make 140 pints of new mix need,

first mix = 140*(6/(6+1)) = 140* (6/7) = 120

second mix = 140*(1/(6+1)) = 140*(1/7) = 20

Hence 120 pints of first mixture and 20 pints of second mixture need to make 140 pints new mixture that 70% pure fruit juice.

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Answer:

Step-by-step explanation:

The given triangles DEF and LNM are similar "by the SSS similarity postulate"

As given in the question, for LNM:

∠N=90°, LN(base)=5 and MN(prependicular)=3

and for DEF:

∠E=90°, DE(base)=10 and MN(prependicular)=6

Two triangles are similar when all their corresponding angles are congruent.

So far we have ∠N≅∠E=90°

Now, for the remaining angles, we first compare ∠L and ∠D.

From Pythagoras' theorem, we get:

For triangle LNM

[tex]LM^{2}=MN^{2}+LN^{2}\\LM=\sqrt{3^{2}+5^{2}}\\LM=\sqrt{34}[/tex]

For triangle DEF

[tex]DF^{2}=EF^{2}+DE^{2}\\DF=\sqrt{6^{2}+10^{2}}\\DF=\sqrt{136}\\DF=2\sqrt{34}[/tex]

Now we have all sides for both triangles and we compare the ratio of corresponding sides;

Side 1: LN:DE = 5:10 = 1:2

Side 2: MN:FE = 3:6 = 1:2

Side 3: LM:DF = [tex]\sqrt{34}[/tex]:[tex]2\sqrt{34}[/tex] = 1:2

As all three ratios are the same, by SSS similarity postulate, we can deduce that triangles LNM and DEF are similar.

This problem can also be solved with the other two (SAS & AA) similarity postulates.

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Answer: Option (C) : Yes, by the SSS Similarity Postulate

Step-by-step explanation:

The perpendicular height of the parallelogram is 13 cm.

A right triangle is a triangle that has an angle that measures 90 degrees. The three sides of a right -angled triangle are known as the length, base and the hypotenuse.

Area of a right-angled triangle = 1/2 x base x height

Area of a right-angled triangle = 1/2 x 13 x 6 = 39 cm²

A parallelogram is quadrilateral that has two pairs of parallel sides. The opposite sides equal in length

Area = base x height

Area of the parallelogram = 4 x 39 = 156 cm²

Height = area / base

156 cm² / 12 = 13 cm

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The two column method can be used to prove that BD is congruent to CE BD ≅ CE as follows;

Statement [tex]{}[/tex]                                            Reasons

1. ΔABC is an isosceles triangle [tex]{}[/tex]       1. Given

2. AB and AC are legs of ΔABC [tex]{}[/tex]       2. Given

3. BD ⊥ DC   [tex]{}[/tex]       [tex]{}[/tex]       [tex]{}[/tex]       [tex]{}[/tex]       [tex]{}[/tex]         3. Given

CE ⊥ BE

4. ∠BDC = 90° and ∠CEB = 90° [tex]{}[/tex]      4. Definition of perpendicular lines

5. ∠BDC = ∠CEB  [tex]{}[/tex]       [tex]{}[/tex]       [tex]{}[/tex]       [tex]{}[/tex]       5. Substitution property

6. ∠BDC ≅ ∠CEB  [tex]{}[/tex]       [tex]{}[/tex]       [tex]{}[/tex]       [tex]{}[/tex]      6. Definition of congruency

7. ∠ABC ≅ ∠ACB [tex]{}[/tex]       [tex]{}[/tex]       [tex]{}[/tex]       [tex]{}[/tex]  7. Base angles of an isosceles triangle

8. [tex]\overline{BC}[/tex] ≅ [tex]\overline{BC}[/tex]  [tex]{}[/tex]       [tex]{}[/tex]       [tex]{}[/tex]       [tex]{}[/tex]       [tex]{}[/tex]       8. Reflexive property of congruency

9. ΔBCE ≅ ΔCBD  [tex]{}[/tex]       [tex]{}[/tex]       [tex]{}[/tex]       [tex]{}[/tex]      9. SAA congruency postulate

10. BD ≅CE [tex]{}[/tex]       [tex]{}[/tex]       [tex]{}[/tex]       [tex]{}[/tex]       [tex]{}[/tex]       [tex]{}[/tex]  10. CPCTC

Two figures are congruent if they have the same size and shape.

The properties, postulates, and theorem used in the prove that BD ≅ CE are as follows;

Perpendicular lines;

Perpendicular lines are lines that form 90° angles where they intersect.

Substitution property

The substitution property of equality states that if one quantity a = b, then b can be substituted for a in equations and expression, such that the value of the expressions and equations remain the same.

Definition of congruency

Congruent figures are figures that have the same shape and size

Base angles of an isosceles triangles

The base angles of an isosceles triangle are congruent

Reflexive property

The reflexive property of congruency states that a figure is congruent to itself

SAA congruency postulate

The Side-Angle-Angle, SAA congruency postulate states that if two angles and  the non included side of one triangle are congruent to two angles and the non included side of the other triangle, then the two triangles are congruent.

CPCTC

Corresponding Parts of Congruent Triangles are Congruent, CPCTC states that the corresponding parts of congruent triangles are also congruent.

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Answer:

Step-by-step explanation: Machine A makes 144 parts in 6 hours. Machine B makes 468 parts in 9 hours. If we divide 144 from 6 we will get 24 parts per hour. 468 divided by 9 would be 52. Now 52 times 12 is 624. 24 times 12 is 288 So if we subtracted 624-288=336.

So Machine B Makes 336 more parts after 12 hours. Hoped this helped!

The perimeter of the rectangular wooden deck, given the measurement of the deck and the addition, can be found to be 18. 8 meters

The perimeter of a rectangular figure can be found by the formula:

= Length + Length + Width + Width

The length was increased by 2. 5 meters and so the new length is:

= 4. 6 + 2. 5

= 7. 1 meters

The new perimeter is therefore:

= 7. 1 + 7. 1 + 2. 3 + 2. 3

= 14. 2 + 4. 6

= 18. 8 meters

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Answer:

Step-by-step explanation:

as

The linear function graphed is defined as follows:

y = -1/3x + 11/3.

The slope-intercept representation of a linear function is given as follows:

y = mx + b

The coefficients of the function and their meaning are listed as follows:

From the graph and from the options, the function crosses the y-axis at y = 11/3, hence the intercept is given as follows:

b = 11/3.

When x increases by 5, from 0 to 5, the function decays from 11/3 to 2, hence the slope is obtained as follows:

m = (2 - 11/3)/5 = (6/3 - 11/3) x 1/5 = -5/3 x 1/5 = -1/3.

Hence the equation is:

y = -1/3x + 11/3.

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(a) k(x) = x-1, m(x) = x+ 2 , n(x) = x - 3  all  shown into the graph .

(b) The degree of the function fn(x) is 3.

(c) The zeros of the function fn(x) is x = 1 , x = -2 and x = 3.

(d)  The intervals over which the value of function f(x) is negative (0,6).

What is function explain?

A function is defined as a relation between a set of inputs having one output each. In simple words, a function is a relationship between inputs where each input is related to exactly one output. Every function has a domain and co-domain or range.

Given that;

k(x) = x - 1

m(x) = x + 2

n(x) = x - 3

[tex]f(x) = k(x)\times m(x)\times n(x)[/tex]

[tex]f(x) = (x-1)\times (x+2)\times (x-3)[/tex]

[tex]f(x) = (x^2+x-2)(x-3)[/tex]

[tex]f(x) = x^3 +x^2-2x-3x^3-3x+6[/tex]

[tex]f(x) = x^3-2x^2-5x+6[/tex]

a) k(x) = x-1,

   m(x) = x+ 2

    n(x) = x - 3

all  shown into the graph .

b)[tex]f(x) = (x-1)\times (x+2)\times (x+3)[/tex]

   [tex]f(x) = x^3-2x^2-5x+6[/tex]

∴degree of function is 3.

degree of function/polynomial is the highest power/degree of the polynomial's monomials.

c) for finding zeros put F(x) = 0 and solve for x

  [tex]f(x) = (x-1)\times (x+2)\times (x-3)\\f(0) = (0-1)\times (0+2)\times (0-3)\\[/tex]

x = 1 , x = -2 and x = 3 are the zeros of f(x).

d) for y-intercept put x = 0

f(0) = (0-1)(0+2)(0-3)

f(0)=6

y-intercept is (0,6).

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