Question 1

Given the function $$f(x) = x^2$, which of the following describes the transformation to obtain g(x$$) = $$-2(x+3)^2 + 5$ from f(x$$)$$?

Accepted Answer

Reflect over the $$x-$$axis, stretch vertically by 2, shift left by 3 units, and up by 5 units.

Question 2

Which of the following functions is even?

Accepted Answer

$$f(x) = 5x^6$ - 3x^2$

Question 3

What is the average rate of change of $$f(x) = x^3$ from x = -2$ to x = 0$?

Accepted Answer

$$-4$$

Question 4

Given the graph of $$f(x) = \sqrt{x}$$, which transformation results in the graph of $$g(x) = -\sqrt{x}$$?

Accepted Answer

Reflection about the $$x-$$axis

Question 5

If a function $$f(x) is $$decreasing on the interval $$(-\infty, 0)$$ and increasing on $$(0, \infty)$$, what can you conclude about $$x=0$$?

Accepted Answer

$$x=0 is a $$relative minimum

Question 6

What is the difference quotient for $$f(x) = 2x^2$?

Accepted Answer

$$4x + 2h$$

Question 7

A man’s height is 57 inches at age 13 and 76 inches at age 18. What is his average rate of change in height over this interval?

Accepted Answer

$$3.8$$ inches/year

Question 8

Which equation represents a line perpendicular to $$y = 2x + 1$$?

Accepted Answer

$$y = -\frac{1}{2}x + 3$$

Question 9

Given the piecewise function $$f(x) = \begin{cases} 3, & x \u003c -1 \ -x^2$, & x \geq -1 \end{cases}$$, what is $$f(-5)$$?

Accepted Answer

$$3$$

Question 10

Which of the following describes the transformation from $$f(x) to$$ $$g(x) = f(x-4) + 2$$?

Accepted Answer

Shift right 4 units and up 2 units

Question 11

Which of the following is the standard form of a linear equation?

Accepted Answer

$$Ax + By = C$$

Question 12

If $$f(x) is an $$odd function, which of the following must be true for all $$x in $$the domain of $$f$$?

Accepted Answer

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

Question 13

Given the graph of $$f(x)$$, which transformation results in the graph of $$y = f(-x)$$?

Accepted Answer

Reflection about the $$y-$$axis

Question 14

Which of the following is the correct formula for the slope between two points $$(x_1$, y_1$)$$ and $$(x_2$, y_2$)$$?

Accepted Answer

$$m = \frac{y_2$ - y_1$}{x_2$ - x_1$}$$

Question 15

Which of the following describes the effect of multiplying a function $$f(x) by a $$constant $$c \u003e 1$$?

Accepted Answer

Vertical stretch

Question 16

Given $$f(x) = x^2$, what is the equation of the graph reflected over the x$-axis and shifted down 3 units?

Accepted Answer

$$y = -x^2$ - 3$$

Question 17

Which of the following is the correct difference quotient for $$f(x) = 6x + 1$$?

Accepted Answer

$$6$$

Question 18

If $$f(x) is $$constant on the interval $$[2, 5]$$, which of the following is true?

Accepted Answer

$$f(x)$$ does not change on $$[2, 5]$$

Functions and Graphs: Core Concepts and Transformations in Precalculus

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