Question 1

Which of the following functions is an odd function?

Accepted Answer

$$f(x) = x^3$

Question 2

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

Accepted Answer

$$-1$$

Question 3

What is the equation of the line in point-slope form that passes through $$(2, -1)$$ with a slope of $$3$$?

Accepted Answer

$$y + 1 = 3(x - 2)$$

Question 4

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

Accepted Answer

$$y = -2x + 4$$

Question 5

What is the slope of a line parallel to the line $$2x - 3y = 6$$?

Accepted Answer

$$\frac{2}{3}$$

Question 6

What is the slope of a line perpendicular to the line $$y = -\frac{1}{2}x + 5$$?

Accepted Answer

$$2$$

Question 7

What is the result of translating the quadratic function $$f(x) = x^2$ two units right and three units down?

Accepted Answer

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

Question 8

Which transformation describes $$g(x) = |x+4| - 2$$ compared to $$f(x) = |x|$$?

Accepted Answer

Shift left 4 units and down 2 units

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 $$(3, -2)$$ and radius $$5$$?

Accepted Answer

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

Question 11

Which of the following is the graph of the circle $$x^2$$ + $$y^2 = 16$?

Accepted Answer

A circle centered at the origin with radius $$4$$

Question 12

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

Accepted Answer

$$(1, 3)$$

Question 13

What is the axis of symmetry for the quadratic function $$f(x) = 2(x+5)^2$ - 7$$?

Accepted Answer

$$x = -5$$

Question 14

Find the zeros of the polynomial $$f(x) = x^2$ - 9.$$

Accepted Answer

$$x = 3, x = -3$$

Question 15

Suppose $$f(x) is a $$continuous function and $$f(1) = -2$$, $$f(3) = 5. $$According to the Intermediate Value Theorem, which of the following must be true?

Accepted Answer

There exists $$c in$$ $$(1, 3)$$ such that $$f(c) = 0$$

Question 16

What is the domain of the function $$f(x) = \sqrt{x-2}$$?

Accepted Answer

$$[2, \infty)$$

Question 17

Given the quadratic function $$f(x) = x^2$ - 4x + 7$$, what is the minimum value of the function?

Accepted Answer

$$3$$

College Algebra Test 2 Study Guide: Functions, Graphs, and Quadratics

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