Question 1

Which of the following describes the transformation applied to the parent function $$f(x) = x^2$ to obtain g(x$$) = $$-(x-3)^2 + 5$?

Accepted Answer

Reflect over the $$x-$$axis, shift right 3 units, shift up 5 units

Question 2

Given the function $$f(x) = -3 - x + 3$$, what is the domain and range of $$f(x)$$?

Accepted Answer

Domain: $$(-\infty, \infty)$$, Range: $$(-\infty, \infty)$$

Question 3

If $$f(x) = 3 - 12x^2$, what is the parent function and what transformation has been applied?

Accepted Answer

Parent: $$x^2$$; vertical stretch by 12, reflection over $$x-$$axis, shift up 3

Question 4

Which of the following best describes the increasing and decreasing intervals of $$f(x) = -(x-3)^2$ + 5$$?

Accepted Answer

Increasing on $$(3, \infty)$$, decreasing on $$(-\infty, 3)$$

Question 5

Given $$g(x) = 2x$$, what are the $$x- $$and $$y-$$intercepts?

Accepted Answer

$$x-$$intercept: $$(0, 0)$$, $$y-$$intercept: $$(0, 0)$$

Question 6

A company models its profit with $$P(x) = -12x^2$ + 3. $$What is the maximum profit and at what value of $$x$$ does it occur?

Accepted Answer

Maximum profit is $$3 at$$ $$x = 0$$

Question 7

Which function represents a reflection over the $$y-$$axis of $$f(x) = x - 3$$?

Accepted Answer

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

Question 8

Given $$f(x) = -1(x-3) - 2$$, what is the slope and $$y-$$intercept of the function?

Accepted Answer

Slope: $$-1$$, $$y-$$intercept: $$1$$

Question 9

A real-world scenario: The height $$h (in $$meters) of a ball thrown upward is modeled by $$h(t) = -4.9t^2$ + 20t + 1.5. $$What is the maximum height the ball reaches?

Accepted Answer

$$21.9$$ meters

Question 10

Which of the following is the correct domain for the function $$f(x) = 3 - 12x^2$?

Accepted Answer

$$(-\infty, \infty)$$

Question 11

If $$f(x) = -3 + 2 - x$$, what is the simplified form of $$f(x)$$?

Accepted Answer

$$f(x) = -x - 1$$

Question 12

Which of the following functions has a minimum value, and at what $$x$$ does it occur?

Accepted Answer

$$f(x) = 3 - 12x^2$; minimum at x$$ = \pm\infty$$

Question 13

Which transformation will change $$f(x) = x^2$ to f(x$$) = $$(x+2)^2 - 5$?

Accepted Answer

Shift left 2 units, shift down 5 units

Question 14

Given $$f(x) = -1(x-3) - 2$$, for which value of $$x$$ does $$f(x) = 0$$?

Accepted Answer

$$x = 1$$

Question 15

Which of the following best describes the range of $$f(x) = -(x-3)^2$ + 5$$?

Accepted Answer

$$(-\infty, 5]$$

Question 16

A population of bacteria is modeled by $$P(t) = 2t. $$What is the population after 5 hours?

Accepted Answer

$$10$$

Question 17

Which function is decreasing for all real numbers?

Accepted Answer

$$f(x) = -x - 1$$

Question 18

If $$f(x) = -3 + 2 - x$$, what is the $$y-$$intercept?

Accepted Answer

$$-1$$

Question 19

Which of the following is the correct set of critical values for $$f(x) = 3 - 12x^2$?

Accepted Answer

$$x = 0$$

Question 20

A car's position is modeled by $$s(t) = 2t. $$What is the average velocity between $$t = 1$$ and $$t = 4$$?

Accepted Answer

$$2$$

Precalculus Study Guide: Graphs and Transformations of Functions

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