Question 1

Which of the following functions is odd?

Accepted Answer

$$f(x) = x^3$

Question 2

Given the piecewise function $$f(x) = \begin{cases} x+2 & 	ext{if } x \u003c 0 \ 2x-1 & 	ext{if } x \geq 0 \end{cases}$$, what is $$f(-3)$$?

Accepted Answer

$$-1$$

Question 3

What is the point-slope form of the equation of a line passing through $$(2, 5)$$ with slope $$-3$$?

Accepted Answer

$$y - 5 = -3(x - 2)$$

Question 4

Which of the following is the slope-intercept form of the line passing through $$(0, 4)$$ with slope $$2$$?

Accepted Answer

$$y = 2x + 4$$

Question 5

What is the slope of a line parallel to the line $$3x - 4y = 7$$?

Accepted Answer

Question 6

What is the equation of a line perpendicular to $$y = -\frac{1}{2}x + 3$$ and passing through $$(4, 1)$$?

Accepted Answer

$$y - 1 = 2(x - 4)$$

Question 7

If $$f(x) = (x-3)^2$ + 2$$, what translation has been performed on the parent function $$f(x) = x^2$?

Accepted Answer

Shifted right 3 units and up 2 units

Question 8

What is the result of reflecting the absolute value function $$f(x) = |x|$$ over the x-axis and shifting it up 4 units?

Accepted Answer

$$f(x) = -|x| + 4$$

Question 9

Find the distance between the points $$(1, 2)$$ and $$(4, 6).$$

Accepted Answer

$$5$$

Question 10

What is the standard form of the equation of a circle with center $$(2, -3)$$ and radius $$5$$?

Accepted Answer

$$(x - 2)^2$ + (y + 3)^2$ = 25$$

Question 11

Which of the following is the graph of a circle centered at $$(0, 0)$$ with radius $$3$$?

Accepted Answer

$$x^2$$ + $$y^2 = 9$

Question 12

Given the quadratic function $$f(x) = -2(x + 1)^2$ + 5$$, what is the axis of symmetry?

Accepted Answer

$$x = -1$$

Question 13

What is the domain of the function $$f(x) = \sqrt{x - 4}$$?

Accepted Answer

$$[4, \infty)$$

Question 14

Find the zeros of the polynomial $$f(x) = x^2$ - 5x + 6.$$

Accepted Answer

$$x = 2, 3$$

Question 15

A function $$f(x) is $$continuous on $$[1, 4]$$ and $$f(1) = -2$$, $$f(4) = 5. $$According to the Intermediate Value Theorem, which of the following must be true?

Accepted Answer

There exists $$c in$$ $$[1, 4]$$ such that $$f(c) = 0$$

Question 16

Given the quadratic function $$f(x) = 2x^2$ - 8x + 3$$, what is the vertex of the parabola?

Accepted Answer

$$(2, -5)$$

Question 17

Which transformation is applied to $$f(x) = \sqrt{x} to $$obtain $$g(x) = \sqrt{x - 6} + 2$$?

Accepted Answer

Shift right 6 units and up 2 units

Question 18

If the equation of a circle is $$x^2$$ + $$y^2 - 4x + 6y = 12$, what is the center of the circle?

Accepted Answer

$$(2, -3)$$

Question 19

What is the range of the quadratic function $$f(x) = -x^2$ + 4x - 1$$?

Accepted Answer

$$(-\infty, 3]$$

College Algebra Test 2 Blueprint: Study Guide

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