Question 1

Given the quadratic function $$f(x) = -3x^2$ + 6x - 1$$, which of the following is the correct vertex of the parabola?

Accepted Answer

$$(1, 2)$$

Question 2

For the function $$f(x) = -3x^2$ + 6x - 1$$, what is the axis of symmetry?

Accepted Answer

$$x = 1$$

Question 3

Given $$f(x) = -3x^2$ + 6x - 1$$, which statement best describes the direction the parabola opens?

Accepted Answer

Downward, because the leading coefficient is negative.

Question 4

If $$f(x) = -3x^2$ + 6x - 1$$, what is the $$y-$$intercept of the function?

Accepted Answer

$$y = -1$$

Question 5

Given $$f(x) = -3x^2$ + 6x - 1$$, which of the following is the domain of $$f$$?

Accepted Answer

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

Question 6

Given $$f(x) = -3x^2$ + 6x - 1$$, what is the range of $$f$$?

Accepted Answer

$$(-\infty, 2]$$

Question 7

Suppose $$f(x) = -3x^2$ + 6x - 1$$ and $$g(x) = \sqrt{x}$$, what is the domain of $$f+g$$?

Accepted Answer

$$[0, \infty)$$

Question 8

Given $$f(x) = -3x^2$ + 6x - 1$$ and $$g(x) = \sqrt{x}$$, what is the formula for $$(f \circ g)(x)$$?

Accepted Answer

$$-3\sqrt{x}^2 + 6\sqrt{x} - 1$$

Question 9

Given $$f(x) = -3x^2$ + 6x - 1$$ and $$g(x) = \sqrt{x}$$, what is the domain of $$(f \circ g)(x)$$?

Accepted Answer

$$[0, \infty)$$

Question 10

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

Accepted Answer

$$3$$

Question 11

Given the piecewise function $$f(x) = \begin{cases} -2x-3 & x \u003c -2 \ x^2$ & -2 \leq x \u003c 2 \ x+5 & x \geq 2 \end{cases}$$, what is $$f(0)$$?

Accepted Answer

$$0$$

Question 12

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

Accepted Answer

$$8$$

Question 13

Given $$f(x) = 3\sqrt{x-4} + 5$$, what is the domain of $$f$$?

Accepted Answer

$$[4, \infty)$$

Question 14

Given $$f(x) = 3\sqrt{x-4} + 5$$, what is the range of $$f$$?

Accepted Answer

$$[5, \infty)$$

Question 15

Given $$f(x) = 3\sqrt{x-4} + 5$$, what is $$f(8)$$?

Accepted Answer

$$11$$

Question 16

Given $$f(x) = 3\sqrt{x-4} + 5$$, solve $$f(x) = 8$$ for $$x.$$

Accepted Answer

$$x = 5$$

Question 17

Write the equation $$x^2$$ + $$y^2 + 6x + 2y + 6 = 0$ in standard form and identify the center and radius of the circle.

Accepted Answer

Center $$(-3, -1)$$, radius $$2$$

Question 18

A rain gutter is to be made from a sheet of aluminum that is 18 inches wide by turning up the edges to form right angles. What is the depth $$x$$ that maximizes the cross-sectional area?

Accepted Answer

$$x = 6$$

College Algebra: Functions, Graphs, and Transformations Study Guide

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