$(-6, 3)$, $(7, 9)$, $(9, \\infty)$

Question 1

Suppose the functions $r(x) = x + 3$ and $s(x) = 2x^2$ are defined for all real numbers $x$. What is $(s - r)(x)$?

Accepted Answer

$2x^2 - x - 3$

Question 2

Given $q(x) = 3x - 1$ and $r(x) = -4x^2 + 1$, what is $(q \circ r)(-5)$?

Accepted Answer

$62$

Question 3

A ball is thrown from a building and its height is modeled by $h = 67 - 5t - 5t^2$. How long after the ball is thrown does it hit the ground?

Accepted Answer

$3.19$ seconds

Question 4

For the quadratic function $f(x) = -2x^2 - 20x - 49$, what is the $x$-coordinate of the vertex?

Accepted Answer

$x = -5$

Question 5

Given the polynomial $w^8 - 6 + 3w + 5w^6$, what is its degree?

Accepted Answer

$8$

Question 6

Suppose the polynomial $f(x) = 4x(x-7)(x+13)^2(x+5)^3$. Which zero has multiplicity three?

Accepted Answer

$-5$

Question 7

The unit cost for producing X-ray machines is given by $C(x) = 0.3x^2 - 150x + 26,424$. How many machines must be made to minimize the unit cost?

Accepted Answer

$250$

Question 8

Which of the following is the correct end behavior for the graph of $f(x) = -x^4 - 2x^2 + 8x^2$?

Accepted Answer

Falls to the left and falls to the right

Question 9

Given the quadratic $y = 2(x+1)(x^2-9)$, which graph best represents this function?

Accepted Answer

Graph C

Question 10

For the function $f(x) = -2x^2 - 20x - 49$, what is the minimum or maximum value of the function?

Accepted Answer

$1$

Question 11

What is the leading coefficient of the polynomial $w^8 - 6 + 3w + 5w^6$?

Accepted Answer

$1$

Question 12

For the function $f(x) = 4x(x-7)(x+13)^2(x+5)^3$, which zero has multiplicity two?

Accepted Answer

$13$

Question 13

Given the function $h = 67 - 5t - 5t^2$, which type of equation best models the height of the ball?

Accepted Answer

Quadratic equation

Question 14

For the polynomial $f(x) = 4x(x-7)(x+13)^2(x+5)^3$, which zero has multiplicity one?

Accepted Answer

$0$

Question 15

Given the function $f(x) = -x^4 - 2x^2 + 8x^2$, what is the sign of the leading coefficient?

Accepted Answer

Negative

Question 16

For the function $f(x) = -2x^2 - 20x - 49$, does the function have a minimum or maximum value?

Accepted Answer

Maximum

Question 17

Given the polynomial $f(x) = 4x(x-7)(x+13)^2(x+5)^3$, how many distinct real zeros does $f(x)$ have?

Accepted Answer

4

Question 18

For the function $f(x) = -x^4 - 2x^2 + 8x^2$, which graph best represents the function?

Accepted Answer

Graph E

Question 19

Given the intervals $(-6, 3)$, $(7, 9)$, and $(9, \infty)$, over which intervals is the function increasing?

Accepted Answer

$(-6, 3)$, $(7, 9)$, $(9, \infty)$

Question 20

Divide $x^2 + 4x + 5$ by $x + 2$. What is the remainder?

Accepted Answer

$1$

College Algebra: Functions, Quadratics, and Polynomials Study Guide

Study Guide - Practice Questions