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Consider the function,
f(1) = 21 - 6
Match each transformation of Rx) with its description.
g() = 21 – 10
9(0) = 21 - 14
g(1) = 81 - 4
g(t) = 21 - 2
g(1) = 81 - 24
g(I) = 85 - 6
shifts 1x) 4 units right
stretches x) by a factor
of 4 away from the x-axis
compresses (x) by a factor
of 4 toward the y-axis
shifts x 4 units down
Answers
Answer:
Shift 4 units down: [tex]g(x) = 2x - 10[/tex]
Stretching f(x) by 4 : [tex]g(x) =8x - 24[/tex]
Shift 4 units left: [tex]g(x) = 2x - 14[/tex]
Compress by 1/4 units : [tex]g(x) = 8x - 6[/tex]
Step-by-step explanation:
Given
[tex]f(x) = 2x - 6[/tex]
Required
Match the transformations (See attachment)
Shift 4 units down
Shifting down a function is represented as:
[tex]g(x) = f(x) - b[/tex]
In this case:
[tex]b = 4[/tex]
Substitute expression for f(x) and 4 for b in [tex]g(x) = f(x) - b[/tex]
[tex]g(x) = 2x - 6 - 4[/tex]
[tex]g(x) = 2x - 10[/tex]
Stretching f(x) by 4
Stretching a function by some units is represented as:
[tex]g(x) =b.f(x)[/tex]
In this case:
[tex]b = 4[/tex]
Substitute expression for f(x) and 4 for b in [tex]g(x) =b.f(x)[/tex]
[tex]g(x) =4 * (2x - 6)[/tex]
[tex]g(x) =8x - 24[/tex]
Shift 4 units left
Shifting a function to the left is represented as:
[tex]g(x) = f(x - b)[/tex]
In this case:
[tex]b = 4[/tex]
Substitute expression for f(x) and 4 for b in [tex]g(x) = f(x - b)[/tex]
[tex]g(x) = f(x-4)[/tex]
Calculating f(x - 4)
[tex]f(x) = 2x - 6[/tex]
[tex]f(x - 4) = 2(x - 4) - 6[/tex]
[tex]f(x - 4) = 2x - 8 - 6[/tex]
[tex]f(x - 4) = 2x - 14[/tex]
Hence:
[tex]g(x) = 2x - 14[/tex]
Compress by 1/4 units
This means that the function is stretched by [tex]1/\frac{1}{4}[/tex]
Compressing a function is represented as:
[tex]g(x) =f(bx)[/tex]
In this case:
[tex]b = 1/\frac{1}{4}[/tex]
[tex]b = 1 * \frac{4}{1}[/tex]
[tex]b = 4[/tex]
Substitute expression for f(x) and 4 for b in [tex]g(x) =f(bx)[/tex]
[tex]g(x) =f(4x)[/tex]
Calculating f(4x)
[tex]f(4x) = 2(4x) - 6[/tex]
[tex]f(4x) = 8x - 6[/tex]
Hence:
[tex]g(x) = 8x - 6[/tex]
Related Questions
What is the equation of the following line? Be sure to scroll down first to see
all answer options.
A. y=-1/2x
B. y=1/4x
C. y=-2x
D. y=1/2x
E. y=2x
F. y=4x
Answers
Answer:
y=-2x
Step-by-step explanation:
A circular "No Parking" road sign has a diameter of 26 inches.
Which measurement is closest to the area of the sign-in square inches?
Answers
Answer: The answer is 530.66
Step-by-step explanation:
I took the test and 81.64 is wrong, It's 530.66
The area of the road sign in the circular shape of diameter 26 inches is closest to 530.66 in².
What is the area of a circle?The area of the circle is pi times the square of the radius of a given circle.
The area of the circle = [tex]\pi r^2[/tex]
A road sign "No Parking" is given in a circular shape of diameter 26 inches. we need to find the area of the sign.
The diameter of the circle is 26 in so, the radius will be half of the diameter which will be 13 in.
Now, the area of the circle = [tex]\pi r^2[/tex]
the area of the circle = 3.14 × 13 × 13
= 530.66 in²
Hence, the area of a circle of diameter 26 inches is equal to 530.66 in².
Learn more about the area of a circle here:
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*will give brainliest to the person who answers first*
At a high school, 9th and 10th graders were asked whether they would prefer
robotics or art as an elective. The results are shown in the relative frequency
table.
To the nearest percent, what percentage of 10th graders surveyed preferred
robotics?
A. 61%
B. 33%
C. 51%
D. 54
Answers
Answer:
33%
Step-by-step explanation:
decimal x 100
please help!! If ED=5, then determine the length of AB
Answers
Answer:
AB equals 25
Step-by-step explanation:
1( you take ED and the 5 and say of 5.
2( then you count all the letters that stand for numbers and count them.
3) after you count them how many ever there are then you take that number which was 5 too.
4(after you find that number which is number 5 you multipliy 5 and 5.
5(after you multipliy then you should get 25 because 5x5 is 25.
And there you go thats the answer step by step.
Recall that for use of a normal distribution as an approximation to the binomial distribution, the conditions np greater than or equal to 5 and nq greater than or equal to 5 must be met. For p= 0.9, compute the minimum sample size needed for use of the normal approximation. Round your answer to the next whole number.
The minimum sample size needed for use of the normal approximation is =
Answers
Answer:
The minimum sample size needed for use of the normal approximation is 50.
Step-by-step explanation:
Suitability of the normal distribution:
In a binomial distribution with parameters n and p, the normal approximation is suitable is:
np >= 5
n(1-p) >= 5
In this question, we have that:
p = 0.9
Since p > 0.5, it means that np > n(1-p). So we have that:
[tex]n(1-p) \geq 5[/tex]
[tex]n(1 - 0.9) \geq 5[/tex]
[tex]0.1n \geq 5[/tex]
[tex]n \geq \frac{5}{0.1}[/tex]
[tex]n \geq 50[/tex]
The minimum sample size needed for use of the normal approximation is 50.
I really need help with this
Answers
explanation
Find the measure of the given angle.
Answers
Answer:
angle UWT=150 degrees
Step-by-step explanation:
angle UWT=360-80-130
angle UWT=150 degrees
Simplify the expression. -2.8+0.3-15-6=
Answers
What is m ZSRW?
- 18
- 54
- 126
- 108
Answers
Answer:
126
Step-by-step explanation:
Angle SRW is supplementary to (2x + 18)º and (3x)º, that is, they add up to 180º.
Finding angles in function of X:
Since angles (2x + 18)º and (3x)º are opposite by vertex R, they have the same measure. So
[tex]3x = 2x + 18[/tex]
[tex]x = 18[/tex]
So
[tex]3x = 3(18) = 54[/tex]
Angle SRW:
Supplementary with 54. So
54 + SRW = 180
SRW = 180 - 54 = 126
So 126 is the answer.
Answer for the question
Answers
Answer:
What is the question?
Step-by-step explanation:
1. Find the area. *
5 ft
5 ft
16 ft
16 ft
Answers
Answer:
25 cm square and 256 cm square
Step-by-step explanation:
Need help ASAP will give brainliest
Answers
Answer:
the second one :)
Step-by-step explanation:
PLS HELP FAST!
A Food Pantry is making packages, Each package weighs 64 pounds.
Scenario 1: Each Package contains 4 identical bags of rice and a 7-pound bag of beans.
a. write an equation to represent the situation using x.
Scenario 2: Each package contains 4 boxes. Each box contains a 7-pound bag of beans and a bag of rice. The bags of rice are all identical.
b. write an equation to represent the situation using x.
I will give brainliest if I figure out how to. I don't know how to. If I figure it out, I will give you one.
Answers
Answer: 4(x) + 7= 64 lbs
Step-by-step explanation:
Scenario 1: 4(x) + 7= 64 lbs
Scenario 2: 4(x) + 7= 64 lbs
2(7-8.5)^2-3|3.5-5|=
Answers
Answer: 0
Step-by-step explanation:
2(7−8.5)2−3(|3.5−5|)
=2(−1.5)2−3(|3.5−5|)
=(2)(2.25)−3(|3.5−5|)
=4.5−3(|3.5−5|)
=4.5−3(|−1.5|)
=4.5−(3)(1.5)
=4.5−4.5
=0
Which phrase represents 3 - 7x
Answers
Answer:
What are the phrases?
Step-by-step explanation:
The table shows the average bill totals for given numbers of diners at Simone's restaurant. If the rate is constant and you graph this relationship with the number of people along the x-axis and bill amounts along the y-axis, which points will lie on the line you get?
a. (12, 470)
b. (20, 800)
c. (24, 1,020)
d. (27, 1,080)
e. (28, 1,110)
Answers
Answer: B and D
Step-by-step explanation: 40 * 20 = 800 and 40 * 27 = 1,080
The point (20 , 800) and ( 27 , 1080 )lies on the line.
Option (b) and (d) is correct.
It is given that average bill totals for given numbers of diners at Simone's restaurant.
To find which points will lie on the line you get.
What is co-ordinate?Coordinates are distances or angles, represented by numbers, that uniquely identify points on surfaces of two dimensions (2D) or in space of three dimensions ( 3D ).
The rate is constant.
Graph this relationship with the number of people along the x-axis and bill amounts along the y axis.
y = mx + c
=> 40 =m+ c
80 = 2m + c
=> m = 40
40 = 40 + c
=> c = 0
Hence
y = 40x
x = 12 => y = 480
x = 20 => y = 800
x =24 => y = 960
x = 27 => y = 1080
x = 28 => y = 1120
Hence (20 , 800) and ( 27 , 1080 ) point lies on the line
Learn more about the co-ordinate here:
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The sum of two odd consecutive integers is 88. Find the integers.
Answers
-- there is an equation to find this: (2n + 1) + (2n + 3) = (whatever number is given as their sum)
use the equation: 2n + 1 is an odd interger, 2n + 3 is the next odd integer.
(2n + 1) + (2n + 3) = 88
add like terms.
4n + 4 = 88
4n = 84
n = 21
now plugin.
2(21) + 1
42 + 1
= 43 (the first odd integer)
this means the second one would be 45.
answer: 43 and 45
add them to check:
43 + 45 = 88
Can someone help!(freckle math)
A crew of highway workers paved 1/3 mile in 1/4 hour. If they work at the same rate,how much will they pave in one hour?
Answers
what is the solution to the division problem below?
Answers
Answer:
there is no division problem
Step-by-step explanation:
Answer:
This may be the work
Step-by-step explanation:
Let f(x) = -2x - 7 and g(x) = -4x + 6. Find (g . f)(-5)
26
3
–59
–6
Answers
Answer:
–59
Step-by-step explanation:
f(x) = -2x - 7
f(x) = -2(-4x + 6) - 7
f(x) = 8x - 12- 7
f(x) = 8x - 19
f(x) = 8(-5) - 19
f(x) = -40 - 19
f(x) = -40 - 19
f(x) = - 59
3x-5y=15 in slope intercept form
Answers
Answer:
I think the answer will be y=3/5x-3
Answer:
y = 3/5x - 3
Step-by-step explanation:
Slope-intercept form is y = mx + b.
For this question, all you need to do is move some stuff around!
In slope intercept form, the x is on the right side, so you would first subtract x from both sides.
3x - 5y = 15
Next, you would divide both sides of the equation by -5 to get y by itself.
-5y = 15 - 3x
Finally, rearrange the equation. y = mx + b
y = -3 + 3/5x
y = 3/5x - 3
Use the expression 1/4p−(1-1/3p). Rewrite the expression without parentheses.Simplify. Show your work. Use a different method to write the expression without parentheses. Do not simplify
Answers
What is the discounted price for a watch that is regularly $58.00 and 30% off?
Answers
Answer:
$40.60
Step-by-step explanation:
Which linear inequality is represented by the graph?
O y s 2x + 4
Oys2x+3
O y z 2 / 3x + 3
O y 22x + 3
Answers
Given:
The graph of an inequality.
To find:
The inequality for the given graph.
Solution:
From the given graph it is clear that the boundary line passes through two point (0,3) and (2,4). So, the equation of boundary line is
[tex]y-y_1=\dfrac{y_2-y_1}{x_2-x_1}(x-x_1)[/tex]
[tex]y-3=\dfrac{4-3}{2-0}(x-0)[/tex]
[tex]y-3=\dfrac{1}{2}(x)[/tex]
[tex]y=\dfrac{1}{2}x+3[/tex]
The shaded area lies below the boundary line and the boundary line is a solid line. So, the sign of inequality must be ≤.
The required inequality is
[tex]y\leq \dfrac{1}{2}x+3[/tex]
Therefore, the correct option is B.
I NEED THIS DONE ASAPPPP
expand 4(m+2)
4(m+2) =
Answers
4(m + 2) expanded is 4 x m and 4 x 2
simplified: 4m + 8
PLEASE HELP!!!
A quadratic equation has two roots: -2 and 3. Which describes the location of the roots on the graph of the equation?
a) at the point (-2,3)
b) crossing the x-axis at -2 and 3
c) at the point (3,-2)
d) crossing the y-axis at -2 and 3
e) at the vertex of the parabola
Answers
Answer:
Answer b) : crossing the x-axis at -2 and 3
Step-by-step explanation:
The roots will be located at the crossing of the graph with the x-axis at the points (-2, 0) and (3, 0).
Therefore, the correct answer is that labeled b)
Erik added 23 new contacts to phone list He had to delete 18 old contacts before could add any more. He now has a total of 100 contacts. Let c represent how many contacts had on phone list before updated it. Write an equation and then solve for c.
Answers
Answer:
c-18+23=100
c=95
Step-by-step explanation:
to prove that the answer is 95 subtract the 18 that she deleted to get 77 then add the 23 that she added after deleting 18 and you get 100
Answer:
c+23−16=100
c=93
Step-by-step explanation:
Juan has 3 blue buttons, 6 red buttons, and 2 yellow buttons in his pocket. All the buttons are the same size and shape. Juan takes out one button. Which statement is correct?
A.
He is more likely to take out a yellow button than a red button.
B.
He is less likely to take out a yellow button than a red button.
C.
He is less likely to take out a red button than a blue button.
D.
He is more likely to take out a blue button than a red button.
I’ll mark you as brainlyest
Answers
Answer: The answer is B
Step-by-step explanation:
Answer:
the answer is B
because in the sentences there less quantity is yellow buttons and more quantity in red button
What is the area of the following circle?
Either enter an exact answer in terms of pie or use 3.143.143, point, 14 for \piπpi and enter your answer as a decimal.
Answers
Answer:
153.86 units²
Step-by-step explanation:
From the question given above, the following data were obtained:
Pi (π) = 3.14
Radius (r) = 7 units
Area (A) =?
The area of a circle can be obtained by using the following formula:
A = πr²
A = 3.14 × 7²
A = 3.14 × 49
A = 153.86 units²
Thus, the area of the circle is 153.86 units²
change 27 km 280m into metre
Answers
Answer:
27,280metres
Step-by-step explanation:
27*1000m+280
27,280m
Answer:
27280
Step-by-step explanation:
1km = 1000 metres
27km = 27000 metres
27000 + 280 =27280 metres
