Question 1

Which of the following equations represents the graph of $$y = x$$ shifted 6 units to the right?

Accepted Answer

$$y = x - 6$$

Question 2

What is the equation of the function $$y = x$$ shifted 8 units upward?

Accepted Answer

$$y = x + 8$$

Question 3

Given the function $$y = x^2$, which equation represents a vertical stretch by a factor of 9?

Accepted Answer

$$y = 9x^2$

Question 4

Suppose the point $$(2, 4) is on $$the graph of $$y = f(x). $$What is a corresponding point on the graph of $$y = 3f(x)$$?

Accepted Answer

$$(2, 12)$$

Question 5

If the x-intercepts of $$y = f(x)$$ are 8 and 3, what are the x-intercepts of $$y = 5f(x)$$?

Accepted Answer

8 and 3

Question 6

Which transformation will result in the graph of $$y = x^2$ being reflected over the y-axis?

Accepted Answer

$$y = (-x)^2$

Question 7

What is the effect of the transformation $$y = |x - 6| - 3 on $$the basic absolute value function $$y = |x|$$?

Accepted Answer

Shift right 6 units and down 3 units

Question 8

Given $$y = f(x)$$, what is the effect of the transformation $$y = f(x + 2) - 1$$?

Accepted Answer

Shift left 2 units and down 1 unit

Question 9

Which equation represents the graph of $$y = x$$ shifted 4 units to the left?

Accepted Answer

$$y = x + 4$$

Question 10

If $$f(x) = x^2$, what is the equation for f(x$$)$$ vertically compressed by a factor of $$\frac{1}{3}$$?

Accepted Answer

$$f(x) = \frac{1}{3}x^2$

Question 11

Suppose $$y = f(x) is an $$even function. Which transformation will always result in a graph that is also even?

Accepted Answer

$$y = f(-x)$$

Question 12

Which transformation would reflect the graph of $$y = f(x)$$ over the x-axis and compress it vertically by a factor of $$\frac{1}{2}$$?

Accepted Answer

$$y = -\frac{1}{2}f(x)$$

Question 13

If $$f(x) = x^3$, what is the equation for f(-x$$)$$?

Accepted Answer

$$f(-x) = (-x)^3$

Question 14

A company models its profit with $$P(x) = x^2$. If the profit function is shifted 5 units downward to account for a new tax, what is the new profit function?

Accepted Answer

$$P(x) = x^2$ - 5$$

Question 15

Given $$y = f(x)$$, which transformation results in a horizontal shift 3 units to the left and a vertical stretch by a factor of 2?

Accepted Answer

$$y = 2f(x + 3)$$

Question 16

If $$y = f(x)$$ has a maximum at $$x = 2$$, where is the maximum for $$y = f(x - 4)$$?

Accepted Answer

$$x = 6$$

Question 17

Which transformation would shift the graph of $$y = \sqrt{x} 5 $$units downward?

Accepted Answer

$$y = \sqrt{x} - 5$$

Question 18

A medical researcher models the spread of a virus with $$N(t) = t^2$. If the model is adjusted to reflect a delay of 3 days, what is the new function?

Accepted Answer

$$N(t) = (t - 3)^2$

Question 19

If $$y = f(x)$$ passes through $$(4, 7)$$, what point is on the graph of $$y = f(x - 2) + 5$$?

Accepted Answer

$$(6, 12)$$

Chapter 2.5

Study Guide - Practice Questions

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