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Algebra Lesson 3-3 Quiz v7

Last updated about 2 years ago

7 questions

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Question 1

1.

Inspect the graph below. What is the value of k?

Question 2

2.

Let f(x)=-6x+2 and h(x)=f(\frac{1}{3}x)+4.

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)?

Question 3

3.

Continuing with the transformation above, we have f(x)=-6x+2 and h(x)=f(\frac{1}{3}x)+4.

Changing the function f into the transformed function h requires both a horizontal stretch by a factor of 3 and vertical translation by 4 units.

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.

Question 4

4.

Select the equations that accurately match the graph.

f(x)=3x-7 \textrm{ and } g(x)=f(\frac{1}{6}x)

f(x)=3x-7 \textrm{ and } g(x)=f(6x)

f(x)=3x-7 \textrm{ and } g(x)=6f(x)

f(x)=3x-7 \textrm{ and } g(x)=\frac{1}{6}f(x)

Question 5

5.

If f(x)=34x+25 and g(x)=f(x-3)+15, which equation defines g(x)?

g(x)=34x-62

g(x)=34x+143

g(x)=31x+25

g(x)=31x+40

Question 6

6.

A spider produces silk for its web at a regular pace, so that the total linear length of silk in centimeters, f(x), is a function of how many hours the spider has been working, x.

When the spider is working normally, the function f is modeled by the equation f(x)= 75x.
When the spider is forced to consume caffine, the quality of the web it weaves deteriorates. But the rate of silk production does increase, from 75 \frac{\textrm{cm}}{\textrm{hr}} to 100 \frac{\textrm{cm}}{\textrm{hr}}.

What type of transformation describes the change from normal silk production to accelarated silk production?

A vertical translation of -25 units

A vertical stretch by a factor of \frac{4}{3}

A vertical stretch by a factor of \frac{3}{4}

A vertical translation of 25 units

Question 7

7.

BONUS: Maximum 2 percentage points

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