Question 1

For the given solution set $$\{2, -1\}$$, write a quadratic equation in general form.

Accepted Answer

$$x^2 - 3x - 2$

Question 2

Find the solution set for the following inequality. Express the answer in interval notation. $$\dfrac{9x + 2}{x - 5} \leq 3x + 2$$

Accepted Answer

$$(-\infty, -1/2]$$

Question 3

Determine if the following relation is a function. If so, find its domain and range: $$\{(1, 11), (1, 22), (3, 8), (3, 10)\}$$

Accepted Answer

Not a function

Question 4

Identify if the given table of $$x$$ and $$y-$$values represents a function. Also, find the domain and range.

$$x$$: $$-5$$, $$-9$$, $$-17$$
$$y$$: $$5$$, $$9$$, $$17$$

Accepted Answer

Function; Domain: $$\{-5, -9, -17\}$$; Range: $$\{5, 9, 17\}$$

Question 5

For the given conditions: Slope $$= -2$$, passing through $$(-3, -1/3)$$, write an equation for the line in slope-intercept form by first going through the point-slope form.

Accepted Answer

$$y = -2x - 19/3$$

Question 6

For a circle with the following center and radius, find its equation (in standard form).
Center $$=(-8, -16)$$, $$r=\sqrt{8}$$

Accepted Answer

$$(x + 8)^2$ + (y + 16)^2$ = 64$$

Question 7

Graph $$h(x) = 3\sqrt{x + 4} as a $$transformation of the square root function $$f(x) = \sqrt{x}.
$$Which of the following describes the transformation?

Accepted Answer

Vertical stretch by 3 and left shift by 4 units

Question 8

Graph the absolute value function $$g(x) = |5x + 5| + \dfrac{3}{2} as a $$transformation of $$f(x) = |5x|. $$Which of the following describes the transformation?

Accepted Answer

Horizontal shift left by 1 and vertical shift up by $$\dfrac{3}{2}$$

Question 9

Given the graphs of $$f(x)$$ and $$g(x)$$, find the value of $$(f - g)(-2).$$

Accepted Answer

$$-3$$

Question 10

Given the two functions $$f$$ and $$g$$, find $$fg$$ and identify the domain.
$$f(x) = 71x - 2$$, $$g(x) = x + 10$$

Accepted Answer

$$fg(x) = 71x^2$ + 712x - 20$$; Domain: $$(-\infty, \infty)$$

Question 11

Find out the equation of the parabola in the vertex form for the given condition:
(a) Shape of the parabola same as $$f(x) = 13x^2$
(b) Vertex of the parabola (-1$$, -1)$$

Accepted Answer

$$y = 13(x + 1)^2$ - 1$$

Question 12

Consider the given polynomial function and plot its graph.
$$f(x) = (x - 17)(x - 29)$$
Which of the following describes the graph?

Accepted Answer

A parabola opening upwards with $$x-$$intercepts at $$x = 17$$ and $$x = 29$$

Question 13

Find the quotient and indicate the remainder, $$r(x)$$, if long division would be performed on the following:
$$4x^5$$ + $$2x^3$$ + $$8x^2$$ \div $$(5x^2 + 3$$)$$

Accepted Answer

$$4x^3/5 + 2x/25 - 8/5 + (6x/25$$ - $$24/5)/(5x^2 + 3$$)$$

Question 14

If $$1 is a $$zero of the following polynomial function, solve for all the other zeros. $$f(x) = x^3$ + 13x^2$ - 14$$

Accepted Answer

$$x = -7 + \sqrt{35}$$ and $$x = -7 - \sqrt{35}$$

Question 15

Determine the end behavior of the graph of the following polynomial function using the Leading Coefficient Test:
$$f(x) = 2x^4$ + 19x^2$ - 3x - 2$$

Accepted Answer

Graph rises to the left and right

Question 16

Graph the given rational function following the seven steps. $$f(x) = \dfrac{7x^2$ - 6x - 16}{4x^2$ - 5x}$$
Which of the following describes the graph?

Accepted Answer

Vertical asymptotes at $$x = 0$$ and $$x = 5/4$$, horizontal asymptote at $$y = 7/4$$

Question 17

The characteristics of the graph of a rational function $$f$$ are given below. Find $$f(x)$$.
$$x-$$intercepts: $$(0, 0)$$
vertical asymptotes: $$x = -2$$ and $$x = 2$$
horizontal asymptote: $$y = 0$$

Accepted Answer

$$f(x) = x/[(x - 2)(x + 2)]$$

Question 18

Complete the given statement using the graph of the rational function in the figure shown.
As $$x 	o 6^-$$, $$f(x) 	o$$

Accepted Answer

As $$x 	o 6^-$$, $$f(x) 	o -\infty$$

College Algebra: Core Concepts, Functions, and Graphs – Study Guide

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