Question 1

Find the x-intercepts of the function.
-$f ( x ) = x ^ { 2 } - 4 x + 3$

Accepted Answer

A) x-intercept: (-3, 0), x-intercept: (-1, 0) 
B)  $\mathrm { x } \text {-intercept: } ( - \sqrt { 3 } , 0 ) , \mathrm { x } \text {-intercept: } ( \sqrt { 3 } , 0 )$ 
C) x-intercept: (1, 0), x-intercept: (2, 0) 
D) x-intercept: (1, 0), x-intercept: (3, 0) 
A) x-intercept: (-3, 0), x-intercept: (-1, 0) 
B)  $\mathrm { x } \text {-intercept: } ( - \sqrt { 3 } , 0 ) , \mathrm { x } \text {-intercept: } ( \sqrt { 3 } , 0 )$ 
C) x-intercept: (1, 0), x-intercept: (2, 0) 
D) x-intercept: (1, 0), x-intercept: (3, 0)

Question 2

Determine the maximum possible number of turning points for the graph of the function.
-$f ( x ) = 5 x ^ { 7 } - 4 x ^ { 6 } - 6 x - 14$

Accepted Answer

A) 5 
B) 7 
C) 0 
D) 6 
A) 5 
B) 7 
C) 0 
D) 6

Question 3

Find all real zeros (estimate the irrational zeros to the nearest hundredth).
-$f ( x ) = x ^ { 4 } + 7 x ^ { 3 } - 7 x ^ { 2 } - 63 x - 18$

Accepted Answer

A) 0.30, -6.70 
B) 3, -3, -0.30, -6.70 
C) 3, -3, 0.30, -6.70 
D) 9, -9, -0.30, -6.70 
A) 0.30, -6.70 
B) 3, -3, -0.30, -6.70 
C) 3, -3, 0.30, -6.70 
D) 9, -9, -0.30, -6.70

Question 4

Use Descartes' Rule of Signs to determine the possible number of positive and negative real zeros for the polynomial
function.
-$f ( x ) = - 4 x ^ { 5 } - 8 x ^ { 4 } - 4 x ^ { 3 } + 3 x ^ { 2 } + x + 16$

Accepted Answer

A) 1 positive zero, 3 or 1 negative zeros 
B) 1 positive zero, 4 or 2 negative zeros 
C) 1 positive zero, 4 or 2 or 0 negative zeros 
D) 1 positive zero, 2 or 0 negative zeros 
A) 1 positive zero, 3 or 1 negative zeros 
B) 1 positive zero, 4 or 2 negative zeros 
C) 1 positive zero, 4 or 2 or 0 negative zeros 
D) 1 positive zero, 2 or 0 negative zeros

Question 5

Graph the rational function.
-$f ( x ) = \frac { 2 } { 1 - 4 x }$

Accepted Answer

A)    
B)    
C)    
D)    
A)    
B)    
C)    
D)

Question 6

Find the real zeros of the function, state their multiplicities if it is a number other than 1.
-$f ( x ) = x ^ { 2 } \left( x ^ { 2 } - 4 \right) \left( x ^ { 2 } + 36 \right)$

Accepted Answer

A)  $x = 0$, multiplicity: 2
$$x = 2 , x = - 2$$ 
B)  $x = 0$, multiplicity: 2
$$\begin{array} { l } 
x = 2 , x = - 2 \
x = 6 , x = - 6
\end{array}$$ 
C)  $x = 0$, multiplicity: 2
$x = - 2$, multiplicity: 2 
D)  $\mathrm { x } = 0$, multiplicity: 2
$x = 2$, multiplicity: 2 
A)  $x = 0$, multiplicity: 2
$$x = 2 , x = - 2$$ 
B)  $x = 0$, multiplicity: 2
$$\begin{array} { l } 
x = 2 , x = - 2 \
x = 6 , x = - 6
\end{array}$$ 
C)  $x = 0$, multiplicity: 2
$x = - 2$, multiplicity: 2 
D)  $\mathrm { x } = 0$, multiplicity: 2
$x = 2$, multiplicity: 2

Question 7

Graph the rational function.
-$f ( x ) = \frac { 5 x - 4 } { 5 x + 10 }$

Accepted Answer

A)    
B)    
C)    
D)    
A)    
B)    
C)    
D)

Question 8

Classify the function as continuous or discontinuous. If the function is not continuous, identify the point(s)of
discontinuity.
-$f ( x ) = \log _ { 4 } ( x + 2 )$

Accepted Answer

A) discontinuous at x = 2 
B) discontinuous at x = -2 
C) continuous 
D) discontinuous at x = 0 
A) discontinuous at x = 2 
B) discontinuous at x = -2 
C) continuous 
D) discontinuous at x = 0

Question 9

Graph the piecewise function.
-$g ( x ) = \left\{ \begin{array} { l l } 
- x - 1 & \text { if } x  - 2
\end{array} \right.$

Accepted Answer

A)    
B)    
C)    
D)    
A)    
B)    
C)    
D)

Question 10

Identify the local maximum and minimum of the graphed function.
-

Accepted Answer

A) local maximum: (-1, 1) 
B) local minimum: (-1, 1)local minimum: (-3, 5)local maximum: (-3, 5) 
C) local minimum: (1, -1) 
D) local maximum: (1, -1)local maximum: (5, -3)local minimum: (5, -3) 
A) local maximum: (-1, 1) 
B) local minimum: (-1, 1)local minimum: (-3, 5)local maximum: (-3, 5) 
C) local minimum: (1, -1) 
D) local maximum: (1, -1)local maximum: (5, -3)local minimum: (5, -3)

Question 11

Classify the function as continuous or discontinuous.
-

Accepted Answer

A) continuous 
B) discontinuous 
A) continuous 
B) discontinuous

Question 12

Determine whether the function is an even function, an odd function, or neither.
-$f ( x ) = 2 x ^ { 2 } + x ^ { 4 }$

Accepted Answer

A) Odd 
B) Even 
C) Neither 
A) Odd 
B) Even 
C) Neither

Question 13

Describe the location, either above the x-axis or below the x-axis, of the graph of the function for large positive values of
x and for large negative values of x.
-$f ( x ) = x ^ { 5 } + x ^ { 4 } + x ^ { 3 } + x ^ { 2 } + x - 3$

Accepted Answer

A) large positive values of x: above x-axis 
B) large positive values of x: below x-axis large negative values of x: below x-axis large negative values of x: below x-axis 
C) large positive values of x: below x-axis 
D) large positive values of x: above x-axis large negative values of x: above x-axis large negative values of x: above x-axis 
A) large positive values of x: above x-axis 
B) large positive values of x: below x-axis large negative values of x: below x-axis large negative values of x: below x-axis 
C) large positive values of x: below x-axis 
D) large positive values of x: above x-axis large negative values of x: above x-axis large negative values of x: above x-axis

Question 14

Determine the minimum degree of the polynomial function graphed.
-$f ( x ) = - 3 x ( x - 2 ) ^ { 2 }$

Accepted Answer

A)    
B)    
C)    
D)    
A)    
B)    
C)    
D)

Question 15

Use the Boundedness Theorem to determine if the zeros of f(x)are bounded over the given interval. If this cannot be
determined, indicate so.
-$f ( x ) = x ^ { 5 } + 2 x ^ { 4 } - 4 x ^ { 3 } + x ^ { 2 } + 17 x - 5 \text { in } [ - 1,2 ]$

Accepted Answer

A) Yes 
B) Cannot determine 
A) Yes 
B) Cannot determine

Question 16

Graph the piecewise function.
-$f ( x ) = \left\{ \begin{array} { l l } 
1 & \text { if } x \geq 1 \
x + 3 & \text { if } x < 1
\end{array} \right.$

Accepted Answer

A)    
B)    
C)    
D)    
A)    
B)    
C)    
D)

Question 17

Determine which of the given graphs could be the graph of the given polynomial function.
-$P ( x ) = - 6 x ^ { 3 } - 3 x ^ { 2 } + 3 x - 2$

Accepted Answer

A)    
B)    
C)    
D)    
A)    
B)    
C)    
D)

Question 18

Classify the function as continuous or discontinuous. If the function is not continuous, identify the point(s)of
discontinuity.
-$$f ( x ) = \frac { 5 x + 2 } { x ^ { 2 } + 4 }$$

Accepted Answer

A) continuous 
B) discontinuous at x = -2 and x = 2 
C)  $\text { discontinuous at } x = - 2 , x = 2 \text { and } x = \frac { 2 } { 5 }$ 
D) discontinuous at x = 4 
A) continuous 
B) discontinuous at x = -2 and x = 2 
C)  $\text { discontinuous at } x = - 2 , x = 2 \text { and } x = \frac { 2 } { 5 }$ 
D) discontinuous at x = 4

Question 19

Find the x-intercepts of the function.
-$f ( x ) = 2 ( x + 4 ) ( x - 5 ) ^ { 3 }$

Accepted Answer

A) x-intercept: (4, 0), x-intercept: (3, 0) 
B) x-intercept: (4, 0), x-intercept: (-5, 0), x-intercept: (3, 0) 
C) x-intercept: (-4, 0), x-intercept: (3, 0) 
D) x-intercept: (-4, 0), x-intercept: (5, 0) 
A) x-intercept: (4, 0), x-intercept: (3, 0) 
B) x-intercept: (4, 0), x-intercept: (-5, 0), x-intercept: (3, 0) 
C) x-intercept: (-4, 0), x-intercept: (3, 0) 
D) x-intercept: (-4, 0), x-intercept: (5, 0)

Question 20

Classify the function as continuous or discontinuous. If the function is not continuous, identify the point(s)of
discontinuity.
-$f ( x ) = 6 ( x + 3 ) ^ { 2 }$

Accepted Answer

A) continuous 
B) discontinuous at x = -3 
C)  $\text { discontinuous at } x = \frac { 1 } { 2 }$ 
D) discontinuous at x = 3 
A) continuous 
B) discontinuous at x = -3 
C)  $\text { discontinuous at } x = \frac { 1 } { 2 }$ 
D) discontinuous at x = 3

Find the x-intercepts of the function. - $f ( x ) = x ^ { 2 } - 4 x + 3$

Determine the maximum possible number of turning points for the graph of the function. - $f ( x ) = 5 x ^ { 7 } - 4 x ^ { 6 } - 6 x - 14$

Find all real zeros (estimate the irrational zeros to the nearest hundredth). - $f ( x ) = x ^ { 4 } + 7 x ^ { 3 } - 7 x ^ { 2 } - 63 x - 18$

Use Descartes' Rule of Signs to determine the possible number of positive and negative real zeros for the polynomial function. - $f ( x ) = - 4 x ^ { 5 } - 8 x ^ { 4 } - 4 x ^ { 3 } + 3 x ^ { 2 } + x + 16$

Graph the rational function. - $f ( x ) = \frac { 2 } { 1 - 4 x }$ $Graph the rational function. - f ( x ) = \frac { 2 } { 1 - 4 x }$

Find the real zeros of the function, state their multiplicities if it is a number other than 1. - $f ( x ) = x ^ { 2 } \left( x ^ { 2 } - 4 \right) \left( x ^ { 2 } + 36 \right)$

Graph the rational function. - $f ( x ) = \frac { 5 x - 4 } { 5 x + 10 }$ $Graph the rational function. - f ( x ) = \frac { 5 x - 4 } { 5 x + 10 }$

Classify the function as continuous or discontinuous. If the function is not continuous, identify the point(s)of discontinuity. - $f ( x ) = \log _ { 4 } ( x + 2 )$

Identify the local maximum and minimum of the graphed function. -

Classify the function as continuous or discontinuous. -

Determine whether the function is an even function, an odd function, or neither. - $f ( x ) = 2 x ^ { 2 } + x ^ { 4 }$

Describe the location, either above the x-axis or below the x-axis, of the graph of the function for large positive values of x and for large negative values of x. - $f ( x ) = x ^ { 5 } + x ^ { 4 } + x ^ { 3 } + x ^ { 2 } + x - 3$

Determine the minimum degree of the polynomial function graphed. - $f ( x ) = - 3 x ( x - 2 ) ^ { 2 }$ $Determine the minimum degree of the polynomial function graphed. - f ( x ) = - 3 x ( x - 2 ) ^ { 2 }$

Use the Boundedness Theorem to determine if the zeros of f(x)are bounded over the given interval. If this cannot be determined, indicate so. - $f ( x ) = x ^ { 5 } + 2 x ^ { 4 } - 4 x ^ { 3 } + x ^ { 2 } + 17 x - 5 \text { in } [ - 1,2 ]$

Graph the piecewise function. - $f ( x ) = \left\{ \begin{array} { l l } 1 & \text { if } x \geq 1 \\x + 3 & \text { if } x < 1\end{array} \right.$ $Graph the piecewise function. - f ( x ) = \left\{ \begin{array} { l l } 1 & \text { if } x \geq 1 \\ x + 3 & \text { if } x < 1 \end{array} \right.$

Determine which of the given graphs could be the graph of the given polynomial function. - $P ( x ) = - 6 x ^ { 3 } - 3 x ^ { 2 } + 3 x - 2$

Classify the function as continuous or discontinuous. If the function is not continuous, identify the point(s)of discontinuity. - $f ( x ) = \frac { 5 x + 2 } { x ^ { 2 } + 4 }$

Find the x-intercepts of the function. - $f ( x ) = 2 ( x + 4 ) ( x - 5 ) ^ { 3 }$

Classify the function as continuous or discontinuous. If the function is not continuous, identify the point(s)of discontinuity. - $f ( x ) = 6 ( x + 3 ) ^ { 2 }$

Basic Concepts

Equations and Inequalities

Graphs and Functions

Systems of Equations and Inequalities

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Exam 10: Characteristics of Functions and Their Graphs

Find the x-intercepts of the function. - f(x)=x2−4x+3f ( x ) = x ^ { 2 } - 4 x + 3f(x)=x2−4x+3

Determine the maximum possible number of turning points for the graph of the function. - f(x)=5x7−4x6−6x−14f ( x ) = 5 x ^ { 7 } - 4 x ^ { 6 } - 6 x - 14f(x)=5x7−4x6−6x−14

Find all real zeros (estimate the irrational zeros to the nearest hundredth). - f(x)=x4+7x3−7x2−63x−18f ( x ) = x ^ { 4 } + 7 x ^ { 3 } - 7 x ^ { 2 } - 63 x - 18f(x)=x4+7x3−7x2−63x−18

Use Descartes' Rule of Signs to determine the possible number of positive and negative real zeros for the polynomial function. - f(x)=−4x5−8x4−4x3+3x2+x+16f ( x ) = - 4 x ^ { 5 } - 8 x ^ { 4 } - 4 x ^ { 3 } + 3 x ^ { 2 } + x + 16f(x)=−4x5−8x4−4x3+3x2+x+16

Graph the rational function. - f(x)=21−4xf ( x ) = \frac { 2 } { 1 - 4 x }f(x)=1−4x2​

Find the real zeros of the function, state their multiplicities if it is a number other than 1. - f(x)=x2(x2−4)(x2+36)f ( x ) = x ^ { 2 } \left( x ^ { 2 } - 4 \right) \left( x ^ { 2 } + 36 \right)f(x)=x2(x2−4)(x2+36)

Graph the rational function. - f(x)=5x−45x+10f ( x ) = \frac { 5 x - 4 } { 5 x + 10 }f(x)=5x+105x−4​

Classify the function as continuous or discontinuous. If the function is not continuous, identify the point(s)of discontinuity. - f(x)=log⁡4(x+2)f ( x ) = \log _ { 4 } ( x + 2 )f(x)=log4​(x+2)

Graph the piecewise function. - g(x)={−x−1 if x<−2−2x−2 if x>−2g ( x ) = \left\{ \begin{array} { l l } - x - 1 & \text { if } x < - 2 \\- 2 x - 2 & \text { if } x > - 2\end{array} \right.g(x)={−x−1−2x−2​ if x<−2 if x>−2​

Identify the local maximum and minimum of the graphed function. -

Classify the function as continuous or discontinuous. -

Determine whether the function is an even function, an odd function, or neither. - f(x)=2x2+x4f ( x ) = 2 x ^ { 2 } + x ^ { 4 }f(x)=2x2+x4

Describe the location, either above the x-axis or below the x-axis, of the graph of the function for large positive values of x and for large negative values of x. - f(x)=x5+x4+x3+x2+x−3f ( x ) = x ^ { 5 } + x ^ { 4 } + x ^ { 3 } + x ^ { 2 } + x - 3f(x)=x5+x4+x3+x2+x−3

Determine the minimum degree of the polynomial function graphed. - f(x)=−3x(x−2)2f ( x ) = - 3 x ( x - 2 ) ^ { 2 }f(x)=−3x(x−2)2

Graph the piecewise function. - f(x)={1 if x≥1x+3 if x<1f ( x ) = \left\{ \begin{array} { l l } 1 & \text { if } x \geq 1 \\x + 3 & \text { if } x < 1\end{array} \right.f(x)={1x+3​ if x≥1 if x<1​

Determine which of the given graphs could be the graph of the given polynomial function. - P(x)=−6x3−3x2+3x−2P ( x ) = - 6 x ^ { 3 } - 3 x ^ { 2 } + 3 x - 2P(x)=−6x3−3x2+3x−2

Classify the function as continuous or discontinuous. If the function is not continuous, identify the point(s)of discontinuity. - f(x)=5x+2x2+4f ( x ) = \frac { 5 x + 2 } { x ^ { 2 } + 4 }f(x)=x2+45x+2​

Find the x-intercepts of the function. - f(x)=2(x+4)(x−5)3f ( x ) = 2 ( x + 4 ) ( x - 5 ) ^ { 3 }f(x)=2(x+4)(x−5)3

Classify the function as continuous or discontinuous. If the function is not continuous, identify the point(s)of discontinuity. - f(x)=6(x+3)2f ( x ) = 6 ( x + 3 ) ^ { 2 }f(x)=6(x+3)2

Basic Concepts

Equations and Inequalities

Graphs and Functions

Systems of Equations and Inequalities

Polynomials and Polynomial Functions

Rational Expressions and Equations

Roots, Radicals, and Complex Numbers

Quadratic Functions

Exponential and Logarithmic Functions

Conic Sections

Sequences, Series, and Probability

Filters

Find the x-intercepts of the function. - $f ( x ) = x ^ { 2 } - 4 x + 3$

Determine the maximum possible number of turning points for the graph of the function. - $f ( x ) = 5 x ^ { 7 } - 4 x ^ { 6 } - 6 x - 14$

Find all real zeros (estimate the irrational zeros to the nearest hundredth). - $f ( x ) = x ^ { 4 } + 7 x ^ { 3 } - 7 x ^ { 2 } - 63 x - 18$

Use Descartes' Rule of Signs to determine the possible number of positive and negative real zeros for the polynomial function. - $f ( x ) = - 4 x ^ { 5 } - 8 x ^ { 4 } - 4 x ^ { 3 } + 3 x ^ { 2 } + x + 16$

Graph the rational function. - $f ( x ) = \frac { 2 } { 1 - 4 x }$ $Graph the rational function. - f ( x ) = \frac { 2 } { 1 - 4 x }$

Find the real zeros of the function, state their multiplicities if it is a number other than 1. - $f ( x ) = x ^ { 2 } \left( x ^ { 2 } - 4 \right) \left( x ^ { 2 } + 36 \right)$

Graph the rational function. - $f ( x ) = \frac { 5 x - 4 } { 5 x + 10 }$ $Graph the rational function. - f ( x ) = \frac { 5 x - 4 } { 5 x + 10 }$

Classify the function as continuous or discontinuous. If the function is not continuous, identify the point(s)of discontinuity. - $f ( x ) = \log _ { 4 } ( x + 2 )$

Determine whether the function is an even function, an odd function, or neither. - $f ( x ) = 2 x ^ { 2 } + x ^ { 4 }$

Describe the location, either above the x-axis or below the x-axis, of the graph of the function for large positive values of x and for large negative values of x. - $f ( x ) = x ^ { 5 } + x ^ { 4 } + x ^ { 3 } + x ^ { 2 } + x - 3$

Determine the minimum degree of the polynomial function graphed. - $f ( x ) = - 3 x ( x - 2 ) ^ { 2 }$ $Determine the minimum degree of the polynomial function graphed. - f ( x ) = - 3 x ( x - 2 ) ^ { 2 }$

Graph the piecewise function. - $f ( x ) = \left\{ \begin{array} { l l } 1 & \text { if } x \geq 1 \\x + 3 & \text { if } x < 1\end{array} \right.$ $Graph the piecewise function. - f ( x ) = \left\{ \begin{array} { l l } 1 & \text { if } x \geq 1 \\ x + 3 & \text { if } x < 1 \end{array} \right.$

Determine which of the given graphs could be the graph of the given polynomial function. - $P ( x ) = - 6 x ^ { 3 } - 3 x ^ { 2 } + 3 x - 2$

Classify the function as continuous or discontinuous. If the function is not continuous, identify the point(s)of discontinuity. - $f ( x ) = \frac { 5 x + 2 } { x ^ { 2 } + 4 }$

Find the x-intercepts of the function. - $f ( x ) = 2 ( x + 4 ) ( x - 5 ) ^ { 3 }$

Classify the function as continuous or discontinuous. If the function is not continuous, identify the point(s)of discontinuity. - $f ( x ) = 6 ( x + 3 ) ^ { 2 }$