Question 1

Evaluate the function $$f ( x ) = \left\{ \begin{array} { c } 
9 - 2 x , x  2
\end{array} \right.$$ at f(7).

Accepted Answer

A) f(7)= 61 
B) f(7)= 58 
C) f(7)= 57 
D) f(7)= 59 
E) f(7)= 60 
A) f(7)= 61 
B) f(7)= 58 
C) f(7)= 57 
D) f(7)= 59 
E) f(7)= 60

Question 2

Evaluate q(4)if $$q ( x ) = \frac { 1 } { \left( x ^ { 2 } - 7 \right) }$$ .

Accepted Answer

A) q(4)= $\frac { 1 } { 13 }$ 
B) q(4)= $\frac { 1 } { 11 }$ 
C) q(4)= $\frac{1}{9}$ 
D) q(4)= $\frac { 1 } { 12 }$ 
E) q(4)= $\frac { 1 } { 10 }$ 
A) q(4)= $\frac { 1 } { 13 }$ 
B) q(4)= $\frac { 1 } { 11 }$ 
C) q(4)= $\frac{1}{9}$ 
D) q(4)= $\frac { 1 } { 12 }$ 
E) q(4)= $\frac { 1 } { 10 }$

Question 3

Does the table describe a function? Input value
$$\begin{array} { | l | l | l | l | l | l | } 
\hline \text { Input value } & 2001 & 2002 & 2003 & 2004 & 2005 \
\hline \text { Output value } & 20 & 50 & 20 & 40 & 30 \
\hline
\end{array}$$

Accepted Answer

A) No 
B) Yes 
A) No 
B) Yes

Question 4

Does the table describe a function? Input value
$$\begin{array} { | l | l | l | l | l | l | } 
\hline \text { Input value } & 5 & 10 & 14 & 10 & 5 \
\hline \text { Output value } & - 13 & - 8 & 0 & 8 & 13 \
\hline
\end{array}$$

Accepted Answer

A) Yes 
B) No 
A) Yes 
B) No

Question 5

Which equation does not represent y as a function of x

Accepted Answer

A) 2x = 8y 
B) -4y = -8 
C) 5x2 + 5y = 3 
D) 3x + 6y = -5 
E) 7y2 + 8x = 9 
A) 2x = 8y 
B) -4y = -8 
C) 5x2 + 5y = 3 
D) 3x + 6y = -5 
E) 7y2 + 8x = 9

Question 6

Which of the following equation represents y as a function of x

Accepted Answer

A) y2 = 9 - x 
B) y3 = x + 9 
C) y2 = x + 9 
D) x2 + y = 9 
E) x2 + y2 = 9 
A) y2 = 9 - x 
B) y3 = x + 9 
C) y2 = x + 9 
D) x2 + y = 9 
E) x2 + y2 = 9

Question 7

Which of the following equation does not represent y as a function of x

Accepted Answer

A) y2 = 1 - x 
B) y = x2 + 1 
C) x2 + y = 1 
D) y = x2 + x - 1 
E) y = x2 - 1 
A) y2 = 1 - x 
B) y = x2 + 1 
C) x2 + y = 1 
D) y = x2 + x - 1 
E) y = x2 - 1

Question 8

Complete the table. $$f ( x ) = \left\{ \begin{array} { l } 
- \frac { 1 } { 2 } x + 4 , x \leq 0 \
( x - 2 ) ^ { 2 } , x > 0
\end{array} \right.$$
$$\begin{array} { | l | l | l | l | l | l | } 
\hline x & - 6 & - 4 & 0 & 1 & 4 \
\hline f ( x ) & & & & & \
\hline
\end{array}$$

Accepted Answer

A) $$\begin{array} { | l | l | l | l | l | l | } 
\hline x & - 6 & - 4 & 0 & 1 & 4 \
\hline f ( x ) & 9 & 7 & - 3 & 1 & 4 \
\hline
\end{array}$$ 
B) $$\begin{array} { | l | l | l | l | l | l | } 
\hline x & - 6 & - 4 & 0 & 1 & 4 \
\hline f ( x ) & 7 & 6 & 4 & 3 & 6 \
\hline
\end{array}$$ 
C) $$\begin{array} { | l | l | l | l | l | l | } 
\hline x & - 6 & - 4 & 0 & 1 & 4 \
\hline f ( x ) & 7 & 6 & 4 & 1 & 4 \
\hline
\end{array}$$ 
D) $$\begin{array} { | l | l | l | l | l | l | } 
\hline x & - 6 & - 4 & 0 & 1 & 4 \
\hline f ( x ) & 7 & 6 & 0 & 1 & 4 \
\hline
\end{array}$$ 
E) $$\begin{array} { | l | l | l | l | l | l | } 
\hline x & - 6 & - 4 & 0 & 1 & 4 \
\hline f ( x ) & 7 & 8 & 4 & 4 & 1 \
\hline
\end{array}$$ 
A) $$\begin{array} { | l | l | l | l | l | l | } 
\hline x & - 6 & - 4 & 0 & 1 & 4 \
\hline f ( x ) & 9 & 7 & - 3 & 1 & 4 \
\hline
\end{array}$$ 
B) $$\begin{array} { | l | l | l | l | l | l | } 
\hline x & - 6 & - 4 & 0 & 1 & 4 \
\hline f ( x ) & 7 & 6 & 4 & 3 & 6 \
\hline
\end{array}$$ 
C) $$\begin{array} { | l | l | l | l | l | l | } 
\hline x & - 6 & - 4 & 0 & 1 & 4 \
\hline f ( x ) & 7 & 6 & 4 & 1 & 4 \
\hline
\end{array}$$ 
D) $$\begin{array} { | l | l | l | l | l | l | } 
\hline x & - 6 & - 4 & 0 & 1 & 4 \
\hline f ( x ) & 7 & 6 & 0 & 1 & 4 \
\hline
\end{array}$$ 
E) $$\begin{array} { | l | l | l | l | l | l | } 
\hline x & - 6 & - 4 & 0 & 1 & 4 \
\hline f ( x ) & 7 & 8 & 4 & 4 & 1 \
\hline
\end{array}$$

Question 9

Evaluate the function at the specified value of the independent variable and simplify. $g ( w ) = \left\{ \begin{array} { c } 
- w , w \leq - 1 \
- w ^ { 2 } + 2 w , - 1  1
\end{array} \right.$ g( $- \frac { 1 } { 2 }$ )

Accepted Answer

A) g( $- \frac { 1 } { 2 }$ )= $\frac { 1 } { 2 }$ 
B) g( $- \frac { 1 } { 2 }$ )= $\frac { 5 } { 8 }$ 
C) g( $- \frac { 1 } { 2 }$ )= $- \frac { 7 } { 4 }$ 
D) g( $- \frac { 1 } { 2 }$ )= 5 
E) g( $- \frac { 1 } { 2 }$ )= $- \frac { 5 } { 4 }$ 
A) g( $- \frac { 1 } { 2 }$ )= $\frac { 1 } { 2 }$ 
B) g( $- \frac { 1 } { 2 }$ )= $\frac { 5 } { 8 }$ 
C) g( $- \frac { 1 } { 2 }$ )= $- \frac { 7 } { 4 }$ 
D) g( $- \frac { 1 } { 2 }$ )= 5 
E) g( $- \frac { 1 } { 2 }$ )= $- \frac { 5 } { 4 }$

Question 10

Find all real value of x such that f (x)= 0. $$f ( x ) = \frac { - 9 x + 8 } { 5 }$$

Accepted Answer

A) x = $\frac { 8 } { 9 }$ 
B) x = $\frac { 8 } { 45 }$ 
C) x = ± $\frac { 8 } { 9 }$ 
D) x = $- \frac { 8 } { 9 }$ 
E) x = ± $\frac { 8 } { 45 }$ 
A) x = $\frac { 8 } { 9 }$ 
B) x = $\frac { 8 } { 45 }$ 
C) x = ± $\frac { 8 } { 9 }$ 
D) x = $- \frac { 8 } { 9 }$ 
E) x = ± $\frac { 8 } { 45 }$

Question 11

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

Accepted Answer

A) Non-negative real numbers x except x = 4 
B) All real numbers x except x = 0 
C) Non-negative real numbers x 
D) All real numbers x 
E) All real numbers x such that x > 0 
A) Non-negative real numbers x except x = 4 
B) All real numbers x except x = 0 
C) Non-negative real numbers x 
D) All real numbers x 
E) All real numbers x such that x > 0

Question 12

Let the function $f$ be defined by the equation $y = f ( x )$ ,where $x$ and $f ( x )$ are real numbers.Find the domain of the function $f ( x ) = \sqrt { 6 x ^ { 2 } + 16 }$

Accepted Answer

A) domain: $\left( - \infty , - \frac { 16 } { 36 } \right) \cup \left( \frac { 16 } { 36 } , + \infty \right)$ 
B) domain: $\left( - \infty , - \frac { \sqrt { 16 } } { 6 } \right)$ 
C) domain: $\left( \frac { 16 } { 36 } , + \infty \right)$ 
D) domain: $\left( - \frac { \sqrt { 16 } } { 6 } , \frac { \sqrt { 16 } } { 6 } \right)$ 
E) domain: $\left( - \infty , - \frac { \sqrt { 16 } } { 6 } \right] \cup \left[ \frac { \sqrt { 16 } } { 6 } , + \infty \right)$ 
A) domain: $\left( - \infty , - \frac { 16 } { 36 } \right) \cup \left( \frac { 16 } { 36 } , + \infty \right)$ 
B) domain: $\left( - \infty , - \frac { \sqrt { 16 } } { 6 } \right)$ 
C) domain: $\left( \frac { 16 } { 36 } , + \infty \right)$ 
D) domain: $\left( - \frac { \sqrt { 16 } } { 6 } , \frac { \sqrt { 16 } } { 6 } \right)$ 
E) domain: $\left( - \infty , - \frac { \sqrt { 16 } } { 6 } \right] \cup \left[ \frac { \sqrt { 16 } } { 6 } , + \infty \right)$

Question 13

Does the table describe a function? Input value
$$\begin{array} { | l | l | l | l | l | l | } 
\hline \text { Input value } & - 5 & - 3 & 0 & 3 & 5 \
\hline \text { Output value } & - 3 & - 3 & - 3 & - 3 & - 3 \
\hline
\end{array}$$

Accepted Answer

A) No 
B) Yes 
A) No 
B) Yes

Exam 4: Functions

Evaluate the function f(x)={9−2x,x<−20,−2≤x≤2x2+8,x>2f ( x ) = \left\{ \begin{array} { c } 9 - 2 x , x < - 2 \\0 , \quad - 2 \leq x \leq 2 \\x ^ { 2 } + 8 , x > 2\end{array} \right.f(x)=⎩⎨⎧​9−2x,x<−20,−2≤x≤2x2+8,x>2​ at f(7).

Evaluate q(4)if q(x)=1(x2−7)q ( x ) = \frac { 1 } { \left( x ^ { 2 } - 7 \right) }q(x)=(x2−7)1​ .

Does the table describe a function? Input value Input value 2001 2002 2003 2004 2005 Output value 20 50 20 40 30

Does the table describe a function? Input value Input value 5 10 14 10 5 Output value -13 -8 0 8 13

Which equation does not represent y as a function of x

Which of the following equation represents y as a function of x

Which of the following equation does not represent y as a function of x

Complete the table. f(x)={−12x+4,x≤0(x−2)2,x>0f ( x ) = \left\{ \begin{array} { l } - \frac { 1 } { 2 } x + 4 , x \leq 0 \\( x - 2 ) ^ { 2 } , x > 0\end{array} \right.f(x)={−21​x+4,x≤0(x−2)2,x>0​ x -6 -4 0 1 4 f(x)

Find all real value of x such that f (x)= 0. f(x)=−9x+85f ( x ) = \frac { - 9 x + 8 } { 5 }f(x)=5−9x+8​

Find the domain of the function. f(x)=x−4xf ( x ) = \frac { x - 4 } { \sqrt { x } }f(x)=x​x−4​

Let the function fff be defined by the equation y=f(x)y = f ( x )y=f(x) ,where xxx and f(x)f ( x )f(x) are real numbers.Find the domain of the function f(x)=6x2+16f ( x ) = \sqrt { 6 x ^ { 2 } + 16 }f(x)=6x2+16​

Does the table describe a function? Input value Input value -5 -3 0 3 5 Output value -3 -3 -3 -3 -3

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

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Hyperbolas

Rotation of Conics

Parametric Equations

Polar Coordinates

Polar Equations of Conics

Graphs of Polar Equations

Filters

Evaluate the function $f ( x ) = \left\{ \begin{array} { c } 9 - 2 x , x < - 2 \\0 , \quad - 2 \leq x \leq 2 \\x ^ { 2 } + 8 , x > 2\end{array} \right.$ at f(7).

Evaluate q(4)if $q ( x ) = \frac { 1 } { \left( x ^ { 2 } - 7 \right) }$ .

Complete the table. $f ( x ) = \left\{ \begin{array} { l } - \frac { 1 } { 2 } x + 4 , x \leq 0 \\( x - 2 ) ^ { 2 } , x > 0\end{array} \right.$ x -6 -4 0 1 4 f(x)

Find all real value of x such that f (x)= 0. $f ( x ) = \frac { - 9 x + 8 } { 5 }$

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

Let the function $f$ be defined by the equation $y = f ( x )$ ,where $x$ and $f ( x )$ are real numbers.Find the domain of the function $f ( x ) = \sqrt { 6 x ^ { 2 } + 16 }$