Let f(x)=\frac{3}{4}x-1 and h(x)=\frac{1}{3}f(4x).
A. What is the slope-intercept equation for h(x), (something like h(x)=mx+b)?
B. What is the slope of h(x)?
C. What is the y-intercept of h(x)?
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Question 3
3.
Continuing with the transformation above, we have f(x)=\frac{3}{4}x-1 and h(x)=\frac{1}{3}f(4x).
Changing the function f into the transformed function h requires both a horizontal stretch by a factor of 4 and vertical compression by a factor of \frac{1}{3}.
Which of these two transformations affects the y-intercept, and how so? Explain your answer and add any equations or graphs necessary to make your explanation clear.
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Question 4
4.
Select the equations that accurately match the graph.
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Question 5
5.
If f(x)=\frac{7}{5}x-3 and g(x)=f(x+10), which equation defines g(x)?
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Question 6
6.
A company saves money in a special reserve fund by depositing \$2,000 every week. The account's balance is a function of the number of weeks since this program started.
Scenario A: The company seeds the account with an initial deposit of \$50,000. The total balance after x weeks is modeled by a(x)=2,000x+50,000.
Scenario B: The comany seeds the account with an initial deposit of \$25,000. The total balance after x weeks is modeled by b(x)=2,000x+25,000.
Which of the following describes the transformation from the function a to the function b?
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Question 7
7.
BONUS: Maximum 2 percentage points
Describe the domain and range of the function a(x) from the scenario above.