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

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

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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