Algebra Lesson 3-3 Quiz v6

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)?

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.

Select the equations that accurately match the graph.

If f(x)=\frac{7}{5}x-3 and g(x)=f(x+10), which equation defines g(x)?

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?

BONUS: Maximum 2 percentage points

Describe the domain and range of the function a(x) from the scenario above.