How does the graph of g(x)=
X-5
+2 compare to the graph of the parent function f(x) = ?
g(x) is shifted 5 units left and 2 units up from f(x).
g(x) is shifted 5 units right and 2 units up from f(x).
Og(x) is shifted 5 units left and 2 units down from f(x).
Og(x) is shifted 5 units right and 2 units down from f(x).

Answers

Answer 1

Answer:

B. g(x) is shifted 5 units right and 2 units up from f(x).

Answer 2

g(x) = [tex]\frac{1}{x-5}[/tex] + 2 is compared to the parent function, f(x) = [tex]\frac{1}{x}[/tex] by g(x) is shifted 5 units right and 2 units up from f(x).

What is Translation of Functions?

Translation of functions is defined as the when each point in the original graph is moved by a fixed units in the same direction.

There are horizontal translation and vertical translation of functions.

Given parent function is,

f(x) = [tex]\frac{1}{x}[/tex]

And the translated function is,

g(x) = [tex]\frac{1}{x-5}[/tex] + 2

When f(x) becomes g(x), the first change occurred is [tex]\frac{1}{x}[/tex] changes to [tex]\frac{1}{x-5}[/tex].

That is f(x) changes to f(x-5).

This translation occurs when the function undergoes horizontal translation towards right.

Then [tex]\frac{1}{x-5}[/tex] is translated to [tex]\frac{1}{x-5}[/tex] + 2.

That is, f(x-5) is changed to f(x-5) + 2.

This occurs for the vertical translation towards up.

Hence the translation occurred is g(x) is shifted 5 units right and 2 units up from f(x).

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Related Questions

Several paint mixtures are made by mixing blue paint and white paint. Paint Colors Blue Paint White Paint Mixture A 5 cups 12 cups Mixture B 6 cups 6 cups Mixture C 4 cups 12 cups Mixture D 5 cups 6 cups Which mixture has the highest ratio of blue paint to white paint? mixture A mixture B mixture C mixture D

Answers

The correct answer is option B which is mixture B will have the highest ratio of blue paint.

What is a ratio?

In mathematics, ratios are used to determine the relationship between two numbers it indicates how many times is one number to another number.

The given ratios are:-

Mixture A = [tex]\dfrac{5}{12} = 0.41[/tex]

Mixture B = [tex]\dfrac{6}{6}= 1[/tex]

Mixture C = [tex]\dfrac{4}{12}= 0.33[/tex]

Mixture B = [tex]\dfrac{5}{6}=0.83[/tex]

Here the ratio of mixture B is the highest among all the options available.

Therefore the correct answer is option B which is mixture B will have the highest ratio of blue paint.

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the distance time graph represents a journey made by jo at the speed was jo walking for the first 15 minutes

Answers

The speed that Jo walked for the first 15 minutes is; 6 km/hr

How to Interpret Distance Time Graphs?

The distance - time graph is missing and so i have attached it.

Now, the formula for speed is;

Speed = Distance/time

The distance after 15 minutes from the graph is 1.5km.

Now, 15 minutes when converted to hours is 15/60 = ¹/₄ hr

Thus, the speed that Jo walked for the first 15 minutes is;

Speed = 1.5/(¹/₄)

Speed = 6 km/hr

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When is the best time to round a number in a multi-step problem?

Answers

Answer:

At the end of the multi step problem

What is the vertex of the graph of the function below?
y=x² + 4x-6
A. (2,0)
B. (-2,6)
C. (-2,-10)
D. (2,6)

Answers

I think it is A
Aaaaaaaaaaaaaaaaa

How many solutions does the following equation have?
7(y+3)=5y+8
A. No Solution
B. Exactly One Solution
C. Infinitely many solutions

Answers

B. Exactly one solution

7y +21 = 5y +8
7y +13=5y
13=-2y
-6.5=y

Answer:

B. Exactly One Solution

Step-by-step explanation:

Given:

[tex]7(y+3)=5y+8[/tex]

Expand the brackets:

[tex]\implies 7y + 21 = 5y + 8[/tex]

Subtract 21 from both sides:

[tex]\implies 7y + 21-21 = 5y + 8-21[/tex]

[tex]\implies 7y=5y-13[/tex]

Subtract 5y from both sides:

[tex]\implies 7y-5y=5y-13-5y[/tex]

[tex]\implies 2y=-13[/tex]

Divide both sides by 2:

[tex]\implies \dfrac{2y}{2}=\dfrac{-13}{2}[/tex]

[tex]\implies y=-\dfrac{13}{2}[/tex]

Therefore, the equation has exactly one solution.

Mr. Lopez fruit salad recipe requires 3/4 of a cup of fresh peaches for 1 serving. He uses 9 cups of fresh peaches to prepare the salad. How many servings of the fruit salad did he prepare?

Answers

Answer:

6.75 servings

Step-by-step explanation:

[tex] \frac{3}{4} \times 9 = \frac{27}{4} = 6 \frac{3}{4} = 6.75[/tex]

Answer:

9 servings

Step-by-step explanation:

feel free to ask where you don't understand.

Which statements are true about the linear inequality y > three-fourthsx – 2? select three options.

Answers

The statement that is true about the linear inequality of y > 3/4x - 2 is that the graph intercepts the y-axis at (0, -2).

What is linear inequality?

Linear inequality is defined as the comparison of two values using greater than, less than, greater than or equal to, and less than or equal to.

Using the general formula for linear inequality,

y >mx+ b

y > 3/4x - 2

Where m = slope of the graph

b = interception at y axis

Therefore, the statement that is true about the linear inequality of y > 3/4x - 2 is that the graph intercepts the y-axis at (0, -2).

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PLEASE HELP ME WITH THIS ASAP

Answers

Eddie: $10-3=$7
Marsha: $8+$3=$11

A 10 ft slide will be installed on a playground. The top of the slide will be 8 ft above the ground.

What angle does the slide make with the ground?

Enter your answer in the box. Round your final answer to the nearest degree.

Answers

Answer

12

Step-by-step explanation:

After covering 4/5 of the journey, James found that he has traveled 48 km. How much of the journey is still left?

Answers

Answer:

12 km

Step-by-step explanation:

Let the total distance to be traveled = x

[tex]\sf \dfrac{4}{5} \ of \ the \ journey = 48\\\\[/tex]

        [tex]\sf \dfrac{4}{5}*x = 48\\\\[/tex]

             [tex]x = 48*\dfrac{5}{4}[/tex]

                = 12 * 5

            x = 60 Km

Distance still to traveled = 60 - 48 = 12Km

Explain how to find the constant of proportionality for the ratio of robins to cardinals.

Answers

The constant of proportionality will be 3.

The complete question ks given below:-

Explain how to find the constant of proportionality for the ratio of robins to cardinals. A 2-column table with 4 rows. Column1 is labelled Cardinals with entries 5, 6, 9, and 10. Column 2 is labelled Robins with entries 15, 18, 27, and 30.

What is the ratio?

In mathematics, ratios are used to determine the relationship between two numbers it indicates how many times is one number to another number.

Given data will be arranged as follows:-

robins              15, 18, 27,  30.

cardinals         5, 6, 9, 10.

The constant of proportionality will be calculated by taking a ratio of the data:-

[tex]\dfrac{Cardinals}{Robins} =\dfrac{15}{5}=\dfrac{18}{6}=\dfrac{27}{9}=\dfrac{30}{10}=3[/tex]

Therefore the constant of proportionality will be 3.

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What value represents the vertical translation from the graph of the parent function f(x)=x² to the graph of the function
g(x)=(x+5)²+3?

Answers

Answer: 3

Reason:

Going from x^2 to (x+5)^2 means we shift the graph 5 units to the left.

The +3 at the end shifts the parabola up 3 units. This is because we add 3 to each y value. For instance a point like (0,25) moves to (0,28)

Equation of graph problem

Answers

The parent function y=1/x²

How horizontal shifting of the graph takes place?

If a function f(x) is shifted horizontally by k units the parent function f(x) becomes f(x+ k) where k>0

Here, the parent function y=1/x²

Add 3 to x in the denominator as the graph is shifted to left 3.

and, Add 1 to the fraction, because the graph is shifted up 1 unit.

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A ration of two numbers is equal to 3:8 if the smaller number is 14 find the greatest number

Answers

Answer:

34 and ⅔

Step-by-step explanation:

added in the picture

100 points helpppp now

Solve the inequality hurrry show your work

33+6f<33

Answers

[tex]\quad \huge \quad \quad \boxed{ \tt \:Answer }[/tex]

[tex]\qquad \tt \rightarrow \:f < 0 [/tex]

____________________________________

[tex] \large \tt Solution \: : [/tex]

[tex]\qquad \tt \rightarrow \: 33 + 6f < 33[/tex]

[ subtract 33 on both sides ]

[tex]\qquad \tt \rightarrow \: 33 - 33+ 6f < 33 - 33[/tex]

[tex]\qquad \tt \rightarrow \: 6f < 0[/tex]

[tex]\qquad \tt \rightarrow \: f < 0[/tex]

Answered by : ❝ AǫᴜᴀWɪᴢ ❞

PLEASE HELP ANSWER MY QUESTION ASAP!

Answers

[tex]\quad \huge \quad \quad \boxed{ \tt \:Answer }[/tex]

[tex]\qquad \tt \rightarrow \: a_{33} = 1\degree[/tex]

____________________________________

[tex] \large \tt Solution \: : [/tex]

In a matrix, [tex] \sf a_{ij} [/tex] represents an element in " i " th row and " j " th column.

Henceforth, element [tex] \sf a_{33} [/tex] represents element in 3rd row and 3rd column.

[tex]\qquad \tt \rightarrow \:a_{33} = 1[/tex]

Answered by : ❝ AǫᴜᴀWɪᴢ ❞

Which statement is true about the information in the double line graph?



A. The number of customers at 12:00 was less on Friday than Saturday.
B. There were more customers on Saturday than Friday.
C. The number of customers was less Saturday than Friday at 10:00 a.m. because many customers slept later.
D. The highest number of customers on both days was at 12:00 p.m.

Answers

D because it’s the peak on both the graphs

Answer:

the answer is d as 38 31 which are highest

Step-by-step explanation:

a is false as 38>31 which is on Saturday
b is false as Saturday customers were less we can infer from the last three on Friday
c false as Saturday was 12 people and Friday 6 people

Circle o has a circumference of 28.3 cm. What is the length of the radius r?

Answers

Circumference = 2Pi * r

28.3cm = 2pi * r ( Isolate r )
28.3cm / 2pi = r
R = 4.504

To verify work we can plug 4.504 back into the equations.

Circumference = 2pi*4.504 ~ 28.299 Which is true !

Which of the lines below is a line of symmetry?
O A. Red

B. Yellow
C. Neither
• D. Both

Answers

Answer: D) Both

Detailed Explanation:

Lines of symmetry in a figure are lines that divide the figure into equal parts.

In the given Figure, the Red lines cuts the shape into 2 equal halves vertically and the Yellow line cuts the shape into 2 equal halves diagonally.

Therefore, both the Red and Yellow lines are lines of symmetry.

Both the Red and Yellow lines are lines of symmetry, Option D is correct.

What is Coordinate system?

A coordinate system is a system that uses one or more numbers, or coordinates, to uniquely determine the position of the points or other geometric elements on a manifold such as Euclidean space.

Lines of symmetry in a figure are lines that divide the figure into equal parts.

The given figure is a square as we observe the four sides are equal in the given shape.

In a square, there are four lines of symmetry, each of which divides it into two identical parts.

The symmetry lines of a square are both its diagonals and the lines joining the midpoints of its opposite sides (bisectors).

In the given Figure, the Red lines cuts the shape into 2 equal halves vertically and the Yellow line cuts the shape into 2 equal halves diagonally.

Hence, both the Red and Yellow lines are lines of symmetry, Option D is correct.

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What is the median of the following data set?
(3, 4, 2, 8, 5)
02
03
04
06

Answers

Answer:

4

Step-by-step explanation:

The median is the middle number when the list is sorted from least to greatest or greatest to least.

We make this list to get 2,3,4,5,8 or 8,5,4,3,2 and the middle number in both lists is 4.

Write an expression for the area of the trapezium below.
Expand any brackets and fully simplify your answer.

Answers

This is my hypothesis

Let a and b be real numbers where a b 0. Which of the following functions could represent the graph below?

1f(x) = x(x-a)²(x - b)4

2f(x) = x(x - a)³(x- b)²

3f(x) = x²(x-a)(x- b)²

4f(x) = x²(x-a)5(x- b)

Answers

The polynomial function that could represent the graph is f(x) = x²(x - a)(x - b)² with four turning points

What is an equation?

An equation is an expression that shows the relationship between two or more numbers and variables.

The maximum number of turning points of a polynomial function is always one less than the degree of the function.

Hence the polynomial represented by the graph is of degree 5 since it has 4 turning points. The polynomial function that could represent the graph is f(x) = x²(x - a)(x - b)²

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A fountain sprays water into a pool as part of the filtration system. The projected path of water is modeled by the function given in the table, where x represents the time in seconds since the water left the fountain and f(x) represents the height in feet above the pool’s water line.



How many seconds does the water travel through the air?

–6
1.5
3
5

Answers

The water travels in 3 seconds.

The correct option is (C).

what is function?

An expression, rule, or law that defines a relationship between one variable (the independent variable) and another variable (the dependent variable).

Given information-

x          0       1       2       3      4      5

f(x)     1.5      2     1. 5     0    -2.5   -6

The image of table attached below.

Here, x represents the time (sec) and f(x) represent the height in feet above the pool’s water line.

From the table,

The height of the water started with 1.5 ft above.After one second the water height reached to the 2 feet above.After two seconds the water height reached to the 1.5 feet above.In 3rd second the water height comes down at the pool's water line.

Hence, the water travel through the air for the 3 seconds.

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QUESTION 10, 11, 12 and 13, 40 POINTS FOR CORRECT AWNSER AND WILL BE BRAINLIEST PLS BE FAST!! I WILL DO ANYTHING U WANT

Answers

10. The missing conversion is 20.32 inches

11. Total number of red cars is 34

12. Total number of blue cars is 36

13. Total number of silver cars is 70

What is Ratio?

Ratio is the number of times a quantity is contained more  or less than another in a whole.

Analysis:

10. If 1 inch = 2.54cm

     Then 8 inches = 8 x 2.54cm = 20.32 cm

     First car park: Total number of cars = 60

     ratio of red:blue:silver = 1:2:3

     Total ratio = 1+2+3 = 6

     number of red cars = 1/6 x 60 = 10

     number of blue cars = 2/6 x 60 = 20 cars

     number of silver cars = 3/6 x 60 = 30

   second car park: Total number of cars = 80

    ratio of blue: red: silver = 2:3:5

    total ratio = 2+3+5 = 10

    number of red cars = 3/10 x 80 = 24

    number of blue cars = 2/10 x 80 = 16

    number of silver cars = 5/10 x 80 = 40

11.  Total number of red cars = 10+24 = 34

12.  Total number of blue cars = 20+16 = 36

13.  Total number of silver cars = 30+40 = 70

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Study the table.

x
y
–2
8
–1
2
0
0
1
2
2
8

Which best describes the function represented by the data in the table?
linear with a common ratio of 4
linear with a common second difference of 4
quadratic with a common ratio of 4
quadratic with a common second difference of 4

Answers

Answer:

quadratic with a common second difference of 4

Step-by-step explanation:

quadratic equations: Quadratic equations are the polynomial equations of degree 2 example - a[tex]x^2\\[/tex]+ b[tex]x[/tex] + c = 0.

                               [tex]\begin{array}{cc}x&y\\-2&8\\-1&2\\0&0\\1&2\\2&8\end{array}\right][/tex]

from the table it is clear that,

function is y = 2[tex]x^2\\[/tex]

so the function is not linear as the equation specifies.

formula to find second difference of a quadratic equation:

f(x + 2) - 2f(x + 1) + f(x)

therefore;

[tex]2(x+2)^2[/tex] - [tex]4(x+1)^2[/tex] + [tex]2x^2[/tex]

[tex]2(x^2 + 4x + 4) - 4(x^2 + 2x+ 1 ) + 2x^2[/tex]

[tex]2x^2 + 8x + 8 - 4x^2 - 8x - 4 + 2x^2[/tex]

[tex]4x^2 - 4x^2 + 8x - 8x +8 - 4[/tex]

4

therefore, the answer is quadratic with a common second difference of 4

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Is 50.2 a rational or an irrational number, why?

Answers

Answer:

Rational.

Step-by-step explanation:

[tex]\textbf{A rational number is a real number that can be expressed as}~ \dfrac{p}{q},\\\\\textbf{where}~ p~ \textbf{and}~ q~ \textbf{are integers.}\\\\ \boxed{50.2 = \dfrac{502}{10}}\\\\ \textbf{50.2 can be expressed as a ratio of two integers,}~ \textbf{so it is a rational number.}[/tex]

Consider a quadrilateral with vertices A(2,2) , B(2,5) , C(7,2), and D(7,5). What is the shape and area of quadrilateral ABCD

Answers

Answer:

Shape is rectangle

Area of rectangle = length * width

= 5 * 3

= 15 units²

A = 1/ 7 - 4√3
B = 1/ 7+ 4√3
Find....
A) a² + b²
B) a³ + b³

Answers

The value of a2+b2 = 0.05

The value of a3+b3 = 41.73

Concept: (a+b)2 = a2+b2+2ab

(a-b)2 = a2+b2-2ab

(a+b)3 = a3+b3+3a2b+3ab2

(a-b)3 = a3-b3-3a2b+3ab2

(I) a²+b²=(1/7-4✓3)²+(1/7+4✓3)²

⇒ ( 1/49 - 48) +(1/49 + 48)=(1-2352/49) + (1+2353/49)

⇒ -47.97 +48.02= 0.05

(ii) a³+b³=(1/7-4✓3)³+(1/7+4✓3)³

⇒(-6.78)³ +(7.07)³

⇒-311.66 +353.39= 41.73

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The diameter of a circle is 62cm

by first calculating the radius work out the area of the circle
give your answer in cm² to 1.d.p

Answers

Answer is 3017.5 cm^2
Reason

We know diameter is 62
Radius (r) is 1/2 of diameter so r=31

Formula for area
A= pi r^2
Fill in what we know
A= (3.14) (31^2)
Multiply
A=3017.54
Round to 1 dp
A= 3017.5

Evaluate.
4^3 + 8^2 = ??

Answers

Answer: 128

Step-by-step explanation:

[tex]4^3 = 4*4*4 = 16*4 = 64[/tex]

[tex]8^2 = 8*8 = 64[/tex]

[tex]64+64 = 128[/tex]

Hopes this helps:

Answer: 128


Simplify 4^3 to 64.

64 + 8^2


Simplify 8^2 to 64.

64 + 64


Simplify.

128
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