Question 1

For the function $$f(x) = -3x + 4$$, over which interval is the function decreasing?

Accepted Answer

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

Question 2

Determine whether the function $$f(x) = 4x^2$ - 3 is $$even, odd, or neither.

Accepted Answer

Even

Question 3

Find the average rate of change of $$f(x) = x^2$ - 2 as$$ $$x$$ changes from $$a = -2 to$$ $$b = 1.$$

Accepted Answer

$$-1$$

Question 4

Given $$f(x) = 6x - 5$$, compute $$\frac{f(x+h) - f(x)}{h}$$ for $$h 
eq 0.$$

Accepted Answer

$$6$$

Question 5

Which of the following describes the transformation from $$f(x) = |x| to$$ $$g(x) = -2|x|$$?

Accepted Answer

Stretch vertically by a factor of 2 and reflect across the x-axis

Question 6

Write an equation for a function whose graph is that of $$f(x) = x^2$ vertically stretched by a factor of 2 and reflected across the x-axis.

Accepted Answer

$$f(x) = -2x^2$

Question 7

Given $$f(x) = x^2$, which of the following is the equation for a graph shifted 4 units to the left, vertically stretched by a factor of 6, reflected across the x-axis, and shifted 8 units downward?

Accepted Answer

$$y = -6(x + 4)^2$ - 8$$

Question 8

For the function $$f(x) = x^2$, which transformation results in g(x) = -(x$$ - $$1)^2 + 11$?

Accepted Answer

Shift 1 unit right, reflect across the x-axis, shift 11 units up

Question 9

Given $$f(x) = x$$, what is the equation for the graph reflected across the y-axis, vertically shrunk by a factor of $$\frac{1}{5}$$, reflected across the x-axis, and shifted 2 units upward?

Accepted Answer

$$y = -\frac{1}{5}(-x) + 2$$

Question 10

Find the intervals where the function $$f(x) = 5x^2$ + 2 is $$increasing.

Accepted Answer

$$(0, \infty)$$

Question 11

Given the function $$f(x) = \frac{x}{x^2$ - 3}$$, determine if it is even, odd, or neither.

Accepted Answer

Odd

Question 12

Suppose $$f(x) = -4x^4$ - 3x - 8. Is $$this function even, odd, or neither?

Accepted Answer

Neither

Question 13

Find the average rate of change of $$g(x) = (x - 4)^2$ as x$ changes from a = 3$ to b = 6$.

Accepted Answer

$$1$$

Question 14

Which of the following is the correct transformation to obtain $$g(x) = \frac{1}{x + 11} - 6$$ from $$f(x) = \frac{1}{x}$$?

Accepted Answer

Shift 11 units left and 6 units down

Question 15

Given the graph in $$image_1$$, what is the domain and range of the function?

Accepted Answer

Domain: $$(-\infty, \infty)$$; Range: $$[-3, 3]$$

Question 16

Given the graph in $$image_2$$, what are the x-intercepts?

Accepted Answer

$$-\frac{3}{2}, 2, 4$$

Question 17

For the function $$f(x) = -4$$, over which interval is the function constant?

Accepted Answer

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

Question 18

Suppose $$f(x) = 9. Is $$this function even, odd, or neither?

Accepted Answer

Even

Question 19

Find the average rate of change of $$f(x) = -3x + 9 as$$ $$x$$ changes from $$a = 2 to$$ $$b = 4.$$

Accepted Answer

$$-3$$

Precalculus Worksheet Guidance: Analyzing Functions, Graphs, and Transformations

Study Guide - Practice Questions

Study Guide - Flashcards