Question 1

Find the value(s)of x for which f (x)= g (x). f(x)= x2 + x - 13 g(x)= -5x + 3

Accepted Answer

A) x= -8,2 
B) x= 8,-2 
C) x= -13,1, $\frac { 3 } { 5 }$ 
D) x= -13,-14, $\frac { 3 } { 5 }$ 
E) x= 12, $\frac { 3 } { 5 }$ 
A) x= -8,2 
B) x= 8,-2 
C) x= -13,1, $\frac { 3 } { 5 }$ 
D) x= -13,-14, $\frac { 3 } { 5 }$ 
E) x= 12, $\frac { 3 } { 5 }$ A

Question 2

Evaluate the difference quotient for the function. 
F (x)= 2x - 7

Accepted Answer

A) -7 
B)  $\frac { 7 } { 2 }$ 
C) 7 
D) 2x + 7 
E) 2 
A) -7 
B)  $\frac { 7 } { 2 }$ 
C) 7 
D) 2x + 7 
E) 2 E

Question 3

Evaluate g(t)- g(9)if g(t)= 12t2 - 6t + 3.

Accepted Answer

A) g(t)- g(9)= 12t2 - 918 + 6t 
B) g(t)- g(9)= 6t2 - 918t + 12 
C) g(t)- g(9)= 12t2 - 918t - 6 
D) g(t)- g(9)= 6t2 + 12t - 918 
E) g(t)- g(9)= 12t2 - 6t - 918 
A) g(t)- g(9)= 12t2 - 918 + 6t 
B) g(t)- g(9)= 6t2 - 918t + 12 
C) g(t)- g(9)= 12t2 - 918t - 6 
D) g(t)- g(9)= 6t2 + 12t - 918 
E) g(t)- g(9)= 12t2 - 6t - 918 E

Question 4

Find the domain of the function. 
F(x)= 2x2 + 4x - 5

Accepted Answer

A) All real numbers x such that x > 0 B) All real numbers x C) All real numbers x such that x < 0 D) Non-negative real numbers x E) Non-negative real numbers x except x = 0 A) All real numbers x such that x > 0 B) All real numbers x C) All real numbers x such that x < 0 D) Non-negative real numbers x E) Non-negative real numbers x except x = 0

Question 5

Find the domain of the function. $f ( w ) = \frac { 8 w } { w + 6 }$

Accepted Answer

A) w = -6,w = 0 
B) w = -6 
C) all real numbers w ? -6,w ? 0 
D) all real numbers 
E) all real numbers w ? -6 
A) w = -6,w = 0 
B) w = -6 
C) all real numbers w ? -6,w ? 0 
D) all real numbers 
E) all real numbers w ? -6

Question 6

Complete the table. $$h ( t ) = \frac { 1 } { 2 } | t + 3 |$$
$$\begin{array} { | l | l | l | l | l | l | } 
\hline t & - 11 & - 9 & 0 & - 5 & - 1 \
\hline h ( t ) & & & & & \
\hline
\end{array}$$

Accepted Answer

A) 
$$\begin{array} { | l | l | l | l | l | l | } 
\hline t & - 11 & - 9 & 0 & - 5 & - 1 \
\hline h ( t ) & 3 & 4 & - 3 & 1 & 1 \
\hline
\end{array}$$ 
B) $$\begin{array} { | l | l | l | l | l | l | } 
\hline t & - 11 & - 9 & 0 & - 5 & - 1 \
\hline \ h ( t ) & 4 & 3 & \frac{3}{2}& 1 & 1 \\
\hline
\end{array}$$. 
C) $$\begin{array} { | l | l | l | l | l | l | } 
\hline t & - 11 & - 9 & 0 & - 5 & - 1 \
\hline \ h ( t ) & 4 & 3 & 1 & \frac{3}{2}& 1 \\
\hline
\end{array}$$ 
D) $$\begin{array} { | l | l | l | l | l | l | } 
\hline t & - 11 & - 9 & 0 & - 5 & - 1 \
\hline \ h ( t ) & 4 & 3 & \frac{3}{2}& 1 & 1 \\
\hline
\end{array}$$ 
E) $$\begin{array} { | l | l | l | l | l | l | } 
\hline t & - 11 & - 9 & 0 & - 5 & - 1 \
\hline h ( t ) & 4 & 3 & 0 & 1 & 1 \
\hline
\end{array}$$ 
A) 
$$\begin{array} { | l | l | l | l | l | l | } 
\hline t & - 11 & - 9 & 0 & - 5 & - 1 \
\hline h ( t ) & 3 & 4 & - 3 & 1 & 1 \
\hline
\end{array}$$ 
B) $$\begin{array} { | l | l | l | l | l | l | } 
\hline t & - 11 & - 9 & 0 & - 5 & - 1 \
\hline \ h ( t ) & 4 & 3 & \frac{3}{2}& 1 & 1 \\
\hline
\end{array}$$. 
C) $$\begin{array} { | l | l | l | l | l | l | } 
\hline t & - 11 & - 9 & 0 & - 5 & - 1 \
\hline \ h ( t ) & 4 & 3 & 1 & \frac{3}{2}& 1 \\
\hline
\end{array}$$ 
D) $$\begin{array} { | l | l | l | l | l | l | } 
\hline t & - 11 & - 9 & 0 & - 5 & - 1 \
\hline \ h ( t ) & 4 & 3 & \frac{3}{2}& 1 & 1 \\
\hline
\end{array}$$ 
E) $$\begin{array} { | l | l | l | l | l | l | } 
\hline t & - 11 & - 9 & 0 & - 5 & - 1 \
\hline h ( t ) & 4 & 3 & 0 & 1 & 1 \
\hline
\end{array}$$

Question 7

Evaluate f(-7)if f(x)= 12x - 8.

Accepted Answer

A) f(-7)= -89 
B) f(-7)= -91 
C) f(-7)= -88 
D) f(-7)= -92 
E) f(-7)= -90 
A) f(-7)= -89 
B) f(-7)= -91 
C) f(-7)= -88 
D) f(-7)= -92 
E) f(-7)= -90

Question 8

Which set of ordered pairs represents a function from A to B
A = {a,b,c} and B = {4,3,1,2}

Accepted Answer

A) {(a,4), (b,3)} 
B) {(a,2), (c,3), (b,4 )} 
C) {(a,4), (c,1)} 
D) {(a,1), (c,3), (c,1), (b,4)} 
E) {(a,4), (c,3), (c,1), (b,1)} 
A) {(a,4), (b,3)} 
B) {(a,2), (c,3), (b,4 )} 
C) {(a,4), (c,1)} 
D) {(a,1), (c,3), (c,1), (b,4)} 
E) {(a,4), (c,3), (c,1), (b,1)}

Question 9

Find all real values of x such that f(x)= 0. 
F(x)= 12 - 2x

Accepted Answer

A) x = 6 
B) x = 5 
C) x = 7 
D) x = 4 
E) x = 8 
A) x = 6 
B) x = 5 
C) x = 7 
D) x = 4 
E) x = 8

Question 10

Evaluate the function at the specified value of the independent variable and simplify. g(s)= 3s + 1G(-18)

Accepted Answer

A) g(-18)= -55 
B) g(-18)= -54s + 3 
C) g(-18)= -18s - 1 
D) g(-18)= -18s + 1 
E) g(-18)= -53 
A) g(-18)= -55 
B) g(-18)= -54s + 3 
C) g(-18)= -18s - 1 
D) g(-18)= -18s + 1 
E) g(-18)= -53

Question 11

Evaluate f(0)if $$f ( x ) = \left\{ \begin{array} { l l } 
9 x + 6 , & x < 0 \
9 x + 9 , & x \geq 0
\end{array} \right.$$ .

Accepted Answer

A) f(0)= -9 
B) f(0)= 6 
C) f(0)= 9 
D) f(0)= -6 
E) f(0)= 0 
A) f(0)= -9 
B) f(0)= 6 
C) f(0)= 9 
D) f(0)= -6 
E) f(0)= 0

Question 12

Complete the table. $$f ( s ) = \frac { | s - 2 | } { s - 2 }$$ 
$$\begin{array} { | l | l | l | l | l | l | } 
\hline \ s & 0 & 4 & \frac { 9 } { 2 } & \frac { 13 } { 2 } & 7 \\
\hline f ( s ) & & & & & \
\hline
\end{array}$$

Accepted Answer

A) $$\begin{array} { | l | l | l | l | l | l | } 
\hline \ s & 0 & 4 & \frac { 9 } { 2 } & \frac { 13 } { 2 } & 7 \\
\hline f ( s ) & - 1 & 1 & 1 & 1 & 1\
\hline
\end{array}$$ 
B) $$\begin{array} { | l | l | l | l | l | l | } 
\hline \s & 0 & 4 & \frac { 9 } { 2 } & \frac { 13 } { 2 } & 7 \\
\hline f ( s ) & - 1 & 1 & 1 & 3&1 \
\hline
\end{array}$$ 
C) $$\begin{array} { | l | l | l | l | l | l | } 
\hline \s & 0 & 4 & \frac { 9 } { 2 } & \frac { 13 } { 2 } & 7 \\
\hline f ( s ) & - 1 & 1 & 3 & 1&1 \
\hline
\end{array}$$ 
D) $$\begin{array} { | l | l | l | l | l | l | } 
\hline \s & 0 & 4 & \frac { 9 } { 2 } & \frac { 13 } { 2 } & 7 \\
\hline f ( s ) & 1 & 1 & 3 & 1&1 \
\hline
\end{array}$$ 
E) $$\begin{array} { | l | l | l | l | l | l | } 
\hline \s & 0 & 4 & \frac { 9 } { 2 } & \frac { 13 } { 2 } & 7 \\
\hline f ( s ) & - 1 & 3 & 1 & 1&1 \
\hline
\end{array}$$ 
A) $$\begin{array} { | l | l | l | l | l | l | } 
\hline \ s & 0 & 4 & \frac { 9 } { 2 } & \frac { 13 } { 2 } & 7 \\
\hline f ( s ) & - 1 & 1 & 1 & 1 & 1\
\hline
\end{array}$$ 
B) $$\begin{array} { | l | l | l | l | l | l | } 
\hline \s & 0 & 4 & \frac { 9 } { 2 } & \frac { 13 } { 2 } & 7 \\
\hline f ( s ) & - 1 & 1 & 1 & 3&1 \
\hline
\end{array}$$ 
C) $$\begin{array} { | l | l | l | l | l | l | } 
\hline \s & 0 & 4 & \frac { 9 } { 2 } & \frac { 13 } { 2 } & 7 \\
\hline f ( s ) & - 1 & 1 & 3 & 1&1 \
\hline
\end{array}$$ 
D) $$\begin{array} { | l | l | l | l | l | l | } 
\hline \s & 0 & 4 & \frac { 9 } { 2 } & \frac { 13 } { 2 } & 7 \\
\hline f ( s ) & 1 & 1 & 3 & 1&1 \
\hline
\end{array}$$ 
E) $$\begin{array} { | l | l | l | l | l | l | } 
\hline \s & 0 & 4 & \frac { 9 } { 2 } & \frac { 13 } { 2 } & 7 \\
\hline f ( s ) & - 1 & 3 & 1 & 1&1 \
\hline
\end{array}$$

Question 13

Find all real value of x such that f (x)= 0. f(x)= 64x2 - 36

Accepted Answer

A) x = ± $\frac { 4 } { 3 }$ 
B) x = ± $\frac { 3 } { 4 }$ 
C) x = - $\frac { 9 } { 16 }$ 
D) x = $\frac { 4 } { 3 }$ 
E) x = ± $\frac { 9 } { 16 }$ 
A) x = ± $\frac { 4 } { 3 }$ 
B) x = ± $\frac { 3 } { 4 }$ 
C) x = - $\frac { 9 } { 16 }$ 
D) x = $\frac { 4 } { 3 }$ 
E) x = ± $\frac { 9 } { 16 }$

Question 14

Let the function f be defined by the equation y = f (x),where x and f (x)are real numbers.Find the domain and range of the function $f ( x ) = \sqrt { 25 x ^ { 2 } - 3 }$ .

Accepted Answer

A) domain: $\left( - \infty , - \frac { 3 } { 25 } \right)$ 
B) domain: $\left( - \frac { 3 } { 5 } , \frac { 3 } { 5 } \right)$ 
C) domain: $\left( - \infty , - \frac { 3 } { 25 } \right] \cup \left[ \frac { 3 } { 25 } , + \infty \right)$ 
D) domain: $\left( \frac { \sqrt { 3 } } { 5 } , + \infty \right)$ 
E) domain: $\left( - \infty , - \frac { \sqrt { 3 } } { 5 } \right] \cup \left[ \frac { \sqrt { 3 } } { 5 } , + \infty \right)$ 
A) domain: $\left( - \infty , - \frac { 3 } { 25 } \right)$ 
B) domain: $\left( - \frac { 3 } { 5 } , \frac { 3 } { 5 } \right)$ 
C) domain: $\left( - \infty , - \frac { 3 } { 25 } \right] \cup \left[ \frac { 3 } { 25 } , + \infty \right)$ 
D) domain: $\left( \frac { \sqrt { 3 } } { 5 } , + \infty \right)$ 
E) domain: $\left( - \infty , - \frac { \sqrt { 3 } } { 5 } \right] \cup \left[ \frac { \sqrt { 3 } } { 5 } , + \infty \right)$

Question 15

Which set of ordered pairs represents a function from P to Q? P = {5,10,15,20} Q = {-1,1,3}

Accepted Answer

A) {(5,3), (15,1), (5,-1), (15,3)} 
B) {(15,-1), (15,1), (15,3)} 
C) {(5,-1), (10,1), (10,3), (15,1), (20,-1)} 
D) {(15,1), (10,-1), (5,1), (10,3), (15,-1)} 
E) {(5,-1), (10,1), (15,3), (20,-1)} 
A) {(5,3), (15,1), (5,-1), (15,3)} 
B) {(15,-1), (15,1), (15,3)} 
C) {(5,-1), (10,1), (10,3), (15,1), (20,-1)} 
D) {(15,1), (10,-1), (5,1), (10,3), (15,-1)} 
E) {(5,-1), (10,1), (15,3), (20,-1)}

Question 16

Evaluate g(s + 2)if g(y)= 12 - 5y.

Accepted Answer

A) g(s + 2)= -2 + 5s 
B) g(s + 2)= -2 - 5s 
C) g(s + 2)= 2 + 5s 
D) g(s + 2)= 2 - 5s 
E) g(s + 2)= 12 - 5s 
A) g(s + 2)= -2 + 5s 
B) g(s + 2)= -2 - 5s 
C) g(s + 2)= 2 + 5s 
D) g(s + 2)= 2 - 5s 
E) g(s + 2)= 12 - 5s

Question 17

A rectangle is bounded by the x-axis and the semicircle $y = \sqrt { 49 - x ^ { 2 } }$ (see figure).Select the area A of the rectangle as a function of x,and determine the domain of the function.?

Accepted Answer

A)  $A ( x ) = 2 | x | \sqrt { 49 - x ^ { 2 } }$,-7 ? x ? 7 
B)  $A ( x ) = - 2 x \sqrt { 49 - x ^ { 2 } }$ ,-7 ? x? 7 
C)  $A ( x ) = x \sqrt { 49 - x ^ { 2 } }$ ,x ? 0 
D)  $A ( x ) = 2 x \sqrt { 49 - x ^ { 2 } }$ ,x ? 0 
E)  $A ( x ) = | x | \sqrt { 49 - x ^ { 2 } }$ ,all real numbers 
A)  $A ( x ) = 2 | x | \sqrt { 49 - x ^ { 2 } }$,-7 ? x ? 7 
B)  $A ( x ) = - 2 x \sqrt { 49 - x ^ { 2 } }$ ,-7 ? x? 7 
C)  $A ( x ) = x \sqrt { 49 - x ^ { 2 } }$ ,x ? 0 
D)  $A ( x ) = 2 x \sqrt { 49 - x ^ { 2 } }$ ,x ? 0 
E)  $A ( x ) = | x | \sqrt { 49 - x ^ { 2 } }$ ,all real numbers

Question 18

Find the domain of the function.$$f ( x ) = \frac { \sqrt { x + 4 } } { 4 + x }$$

Accepted Answer

A) Non-negative real numbers x B) All real numbers x C) All real numbers x such that x > -4 D) Non-negative real numbers x except x =4 E) All real numbers x such that x < 4 A) Non-negative real numbers x B) All real numbers x C) All real numbers x such that x > -4 D) Non-negative real numbers x except x =4 E) All real numbers x such that x < 4

Question 19

Find all real values of x such that f(x)= 0. $f ( x ) = \frac { 5 x - 7 } { 3 }$

Accepted Answer

A) x = 2 
B) x = $\frac { 8 } { 5 }$ 
C) x = $\frac{9}{5}$ 
D) x = $\frac { 7 } { 5 }$ 
E) x = $\frac { 11 } { 5 }$ 
A) x = 2 
B) x = $\frac { 8 } { 5 }$ 
C) x = $\frac{9}{5}$ 
D) x = $\frac { 7 } { 5 }$ 
E) x = $\frac { 11 } { 5 }$

Question 20

Find all real values of x such that f(x)= 0
F(x)= x3 - x2 - 9x + 9

Accepted Answer

A) x = 0,3 
B) x = 1,-3 
C) x = 0,-3 
D) x = 1,3 
E) x = 1,±3 
A) x = 0,3 
B) x = 1,-3 
C) x = 0,-3 
D) x = 1,3 
E) x = 1,±3

Exam 4: Functions

Find the value(s)of x for which f (x)= g (x). f(x)= x2 + x - 13 g(x)= -5x + 3

Evaluate the difference quotient for the function. F (x)= 2x - 7

Evaluate g(t)- g(9)if g(t)= 12t2 - 6t + 3.

Find the domain of the function. F(x)= 2x2 + 4x - 5

Find the domain of the function. f(w)=8ww+6f ( w ) = \frac { 8 w } { w + 6 }f(w)=w+68w​

Complete the table. h(t)=12∣t+3∣h ( t ) = \frac { 1 } { 2 } | t + 3 |h(t)=21​∣t+3∣ t -11 -9 0 -5 -1 h(t)

Evaluate f(-7)if f(x)= 12x - 8.

Which set of ordered pairs represents a function from A to B A = {a,b,c} and B = {4,3,1,2}

Find all real values of x such that f(x)= 0. F(x)= 12 - 2x

Evaluate the function at the specified value of the independent variable and simplify. g(s)= 3s + 1G(-18)

Evaluate f(0)if f(x)={9x+6,x<09x+9,x≥0f ( x ) = \left\{ \begin{array} { l l } 9 x + 6 , & x < 0 \\9 x + 9 , & x \geq 0\end{array} \right.f(x)={9x+6,9x+9,​x<0x≥0​ .

Complete the table. f(s)=∣s−2∣s−2f ( s ) = \frac { | s - 2 | } { s - 2 }f(s)=s−2∣s−2∣​ s 0 4 7 f(s)

Find all real value of x such that f (x)= 0. f(x)= 64x2 - 36

Let the function f be defined by the equation y = f (x),where x and f (x)are real numbers.Find the domain and range of the function f(x)=25x2−3f ( x ) = \sqrt { 25 x ^ { 2 } - 3 }f(x)=25x2−3​ .

Which set of ordered pairs represents a function from P to Q? P = {5,10,15,20} Q = {-1,1,3}

Evaluate g(s + 2)if g(y)= 12 - 5y.

A rectangle is bounded by the x-axis and the semicircle y=49−x2y = \sqrt { 49 - x ^ { 2 } }y=49−x2​ (see figure).Select the area A of the rectangle as a function of x,and determine the domain of the function.?

Find the domain of the function. f(x)=x+44+xf ( x ) = \frac { \sqrt { x + 4 } } { 4 + x }f(x)=4+xx+4​​

Find all real values of x such that f(x)= 0. f(x)=5x−73f ( x ) = \frac { 5 x - 7 } { 3 }f(x)=35x−7​

Find all real values of x such that f(x)= 0 F(x)= x3 - x2 - 9x + 9

Rectangular Coordinates

Graphs of Equations

Linear Equations in Two Variables

Analyzing Graphs of Functions

A Library of Parent Functions

Transformations of Functions

Combinations of Functions Composite Functions

Inverse Functions

Mathematical Modeling and Variation

Quadratic Functions and Models

Polynomial Functions of Higher Degree

Polynomial and Synthetic Division

Complex Numbers

Zeros of Polynomial Functions

Rational Functions

Nonlinear Inequalities

Exponential Functions and Their Graphs

Logarithmic Functions and Their Graphs

Properties of Logarithms

Exponential and Logarithmic Equations

Exponential and Logarithmic Models

Radian and Degree Measure

Trigonometric Functions The Unit Circle

Right Triangle Trigonometry

Trigonometric Functions of Any Angle

Graphs of Sine and Cosine Functions

Graphs of Other Trigonometric Functions

Inverse Trigonometric Functions

Applications and Models

Using Fundamental Identities

Verifying Trigonometric Equations

Solving Trigonometric Equations

Sum and Difference Formulas

Multiple Angle and Product to Sum Formulas

Law of Sines

Law of Cosines

Vectors in the Plane

Vectors and Dot Products

Trigonometric Form of a Complex Number

Linear and Nonlinear Systems of Equations

Two Variable Linear Systems

Multivariable Linear Systems

Partial Fractions

Systems of Inequalities

Linear Programming

Matrices and Systems of Equations

Operations With Matrices

The Inverse of a Square Matrix

The Determinant of a Square Matrix

Applications of Matrices and Determinants

Sequences and Series

Arithmetic Sequences and Partial Sums

Geometric Sequences and Series

Mathematical Induction

The Binomial Theorem

Counting Principles

Probability

Lines

Introduction to Conics Parabolas

Find the value(s)of x for which f (x)= g (x). f(x)= x² + x - 13 g(x)= -5x + 3

Evaluate g(t)- g(9)if g(t)= 12t² - 6t + 3.

Find the domain of the function. F(x)= 2x² + 4x - 5

Find the domain of the function. $f ( w ) = \frac { 8 w } { w + 6 }$

Complete the table. $h ( t ) = \frac { 1 } { 2 } | t + 3 |$ t -11 -9 0 -5 -1 h(t)

Evaluate f(0)if $f ( x ) = \left\{ \begin{array} { l l } 9 x + 6 , & x < 0 \\9 x + 9 , & x \geq 0\end{array} \right.$ .

Complete the table. $f ( s ) = \frac { | s - 2 | } { s - 2 }$ s 0 4 7 f(s)

Find all real value of x such that f (x)= 0. f(x)= 64x² - 36

Let the function f be defined by the equation y = f (x),where x and f (x)are real numbers.Find the domain and range of the function $f ( x ) = \sqrt { 25 x ^ { 2 } - 3 }$ .

Find the domain of the function. $f ( x ) = \frac { \sqrt { x + 4 } } { 4 + x }$

Find all real values of x such that f(x)= 0. $f ( x ) = \frac { 5 x - 7 } { 3 }$

Find all real values of x such that f(x)= 0 F(x)= x³ - x² - 9x + 9