Question 1

Identify all intercepts of $f ( x ) = \frac { x ^ { 2 } } { x ^ { 2 } + 16 }$

Accepted Answer

A)  $x$-intercept: $( 0,0 ) ; y$-intercept: $( 0,0 )$ 
B)  $x$-intercepts: $( - 4,0 )$ and $( 4,0 ) ; y$-intercept: $( 0,1 )$ 
C)  $x$-intercept: none; $y$-intercept: none 
D)  $x$-intercept: none; $y$-intercept: $( 0,1 )$ 
E)  $x$-intercept: none; $y$-intercept: $( 0,5 )$ 
A)  $x$-intercept: $( 0,0 ) ; y$-intercept: $( 0,0 )$ 
B)  $x$-intercepts: $( - 4,0 )$ and $( 4,0 ) ; y$-intercept: $( 0,1 )$ 
C)  $x$-intercept: none; $y$-intercept: none 
D)  $x$-intercept: none; $y$-intercept: $( 0,1 )$ 
E)  $x$-intercept: none; $y$-intercept: $( 0,5 )$

Question 2

Use the position equation $s = - 20 t ^ { 2 } + v _ { 0 } t + s _ { 0 }$ , where $S$ represents the height of an object (in feet), $\mathcal { V } _ { 0 }$ represents the initial velocity of the object (in feet per second), $s _ { 0 }$ represents the Initial height of the object (in feet), and $t$ represents the time (in seconds).
A projectile is fired straight upward from ground level $\left( s _ { 0 } = 0 \right)$ with an initial velocity of $220$ feet Per second. At what instant will it be back at ground level?

Accepted Answer

A)  $t = 13 \mathrm { Sec }$ 
B)  $t = 12 \mathrm { Sec }$ 
C)  $t = 20 \mathrm { Sec }$ 
D)  $t = 11 \mathrm { Sec }$ 
E)  $t = 10 \mathrm { Sec }$ 
A)  $t = 13 \mathrm { Sec }$ 
B)  $t = 12 \mathrm { Sec }$ 
C)  $t = 20 \mathrm { Sec }$ 
D)  $t = 11 \mathrm { Sec }$ 
E)  $t = 10 \mathrm { Sec }$

Question 3

Select the graph of the function $y = ( x / 3 ) ^ { 2 } - 5$ . Compare the graph of this function with the graph of $y = x ^ { 2 }$

Accepted Answer

A) 
 
Horizontal stretch and vertical shift. 
B) 
 
Horizontal stretch and vertical shift. 
C) 
 
Horizontal stretch and vertical shift. 
D) 
 
Horizontal stretch and vertical shift. 
E) 
 
Horizontal stretch and vertical shift. 
A) 
 
Horizontal stretch and vertical shift. 
B) 
 
Horizontal stretch and vertical shift. 
C) 
 
Horizontal stretch and vertical shift. 
D) 
 
Horizontal stretch and vertical shift. 
E) 
 
Horizontal stretch and vertical shift.

Question 4

Select the correct graph of the function given by $f ( x ) = x ^ { 4 }$ . Explain how the graph of function g differs (if it does) from the graph of each function $f$. $g ( x ) = f ( x ) + 8$

Accepted Answer

A) 
 
Horizontal shift of eight units to the left 
B) 
 
Vertical shift of eight units 
C) 
 
Horizontal shift of eight units to the right 
D)

Vertically downward shift of eight units 
E)

Horizontal shift of eight units 
A) 
 
Horizontal shift of eight units to the left 
B) 
 
Vertical shift of eight units 
C) 
 
Horizontal shift of eight units to the right 
D)

Vertically downward shift of eight units 
E)

Horizontal shift of eight units

Question 5

Solve the equation and write complex solutions in standard form. $$x ^ { 2 } - 10 x + 41 = 0$$

Accepted Answer

A)  $x = - 20 - 4 i , - 20 + 4 i$ 
B)  $x = - 4 + 5 i , - 4 - 5 i$ 
C)  $x = 5 + 16 i , 5 - 16 i$ 
D)  $x = 5 - 4 i , 5 + 4 i$ 
E)  $x = - 4 + 25 i , - 4 - 25 i$ 
A)  $x = - 20 - 4 i , - 20 + 4 i$ 
B)  $x = - 4 + 5 i , - 4 - 5 i$ 
C)  $x = 5 + 16 i , 5 - 16 i$ 
D)  $x = 5 - 4 i , 5 + 4 i$ 
E)  $x = - 4 + 25 i , - 4 - 25 i$

Question 6

Use the position equation $s = - 20 t ^ { 2 } + v _ { 0 } t + s _ { 0 }$ , where $S$ represents the height of an object (in feet), $v _ { 0 }$ represents the initial velocity of the object (in feet per second), $s _ { 0 }$ represents the Initial height of the object (in feet), and $t$ represents the time (in seconds).
A projectile is fired straight upward from ground level $\left( s _ { 0 } = 0 \right)$ with an initial velocity of $200$ feet Per second. At what instant will it be back at ground level?

Accepted Answer

A)  $t = 10 \mathrm { Sec }$ 
B)  $t = 12 \mathrm { Sec }$ 
C)  $t = 11 \mathrm { Sec }$ 
D)  $t = 9 \mathrm { Sec }$ 
E)  $t = 20 \mathrm { Sec }$ 
A)  $t = 10 \mathrm { Sec }$ 
B)  $t = 12 \mathrm { Sec }$ 
C)  $t = 11 \mathrm { Sec }$ 
D)  $t = 9 \mathrm { Sec }$ 
E)  $t = 20 \mathrm { Sec }$

Question 7

Describe the right-hand and the left-hand behavior of the graph of 
$n ( x ) = - \frac { 8 } { 11 } \left( x ^ { 3 } - 4 x ^ { 2 } + x + 1 \right)$

Accepted Answer

A)  Because the degree is odd and the leading coefficient is negative, the graph rises to the left and falls to the right. 
B)  Because the degree is odd and the leading coefficient is negative, the graph falls to the left and rises to the right. 
C)  Because the degree is odd and the leading coefficient is positive, the graph falls to the left and falls to the right. 
D)  Because the degree is odd and the leading coefficient is positive, the graph rises to the left and rises to the right. 
E)  Because the degree is even and the leading coefficient is negative, the graph rises to the left and falls to the right. 
A)  Because the degree is odd and the leading coefficient is negative, the graph rises to the left and falls to the right. 
B)  Because the degree is odd and the leading coefficient is negative, the graph falls to the left and rises to the right. 
C)  Because the degree is odd and the leading coefficient is positive, the graph falls to the left and falls to the right. 
D)  Because the degree is odd and the leading coefficient is positive, the graph rises to the left and rises to the right. 
E)  Because the degree is even and the leading coefficient is negative, the graph rises to the left and falls to the right.

Question 8

The height, $h ( x )$ , of a punted rugby ball is given by $h ( x ) = \frac { 1 } { 64 } x ^ { 2 } + \frac { 9 } { 16 } x + 3$ where x is the horizontal distance in feet from the point where the ball is punted. How far, horizon- tally, is the ball from the kicker when it is at its highest point?

Accepted Answer

A) 18 feet 
B)  28 feet 
C)  39 feet 
D)  23 feet 
E)  21 feet 
A) 18 feet 
B)  28 feet 
C)  39 feet 
D)  23 feet 
E)  21 feet

Question 9

Find vertical asymptotes of the following function. $g ( x ) = \frac { x - 6 } { x ^ { 2 } - 36 }$

Accepted Answer

A)  $x = 36$ 
B)  $x = - 6$ 
C)  $x = - 36$ 
D)  $x = 6$ 
E)  $x = 0$ 
A)  $x = 36$ 
B)  $x = - 6$ 
C)  $x = - 36$ 
D)  $x = 6$ 
E)  $x = 0$

Identify all intercepts of $f ( x ) = \frac { x ^ { 2 } } { x ^ { 2 } + 16 }$

Select the graph of the function $y = ( x / 3 ) ^ { 2 } - 5$ . Compare the graph of this function with the graph of $y = x ^ { 2 }$

Select the correct graph of the function given by $f ( x ) = x ^ { 4 }$ . Explain how the graph of function g differs (if it does) from the graph of each function $f$ . $g ( x ) = f ( x ) + 8$

Solve the equation and write complex solutions in standard form. $x ^ { 2 } - 10 x + 41 = 0$

Describe the right-hand and the left-hand behavior of the graph of $n ( x ) = - \frac { 8 } { 11 } \left( x ^ { 3 } - 4 x ^ { 2 } + x + 1 \right)$

The height, $h ( x )$ , of a punted rugby ball is given by $h ( x ) = \frac { 1 } { 64 } x ^ { 2 } + \frac { 9 } { 16 } x + 3$ where x is the horizontal distance in feet from the point where the ball is punted. How far, horizon- tally, is the ball from the kicker when it is at its highest point?

Find vertical asymptotes of the following function. $g ( x ) = \frac { x - 6 } { x ^ { 2 } - 36 }$

Functions and Their Graphs

Exponential and Logarithmic Functions

Trigonometry

Analytic Trigonometry

Topics in Analytic Geometry

Filters

Exam 2: Polynomial and Rational Functions

Identify all intercepts of f(x)=x2x2+16f ( x ) = \frac { x ^ { 2 } } { x ^ { 2 } + 16 }f(x)=x2+16x2​

Select the graph of the function y=(x/3)2−5y = ( x / 3 ) ^ { 2 } - 5y=(x/3)2−5 . Compare the graph of this function with the graph of y=x2y = x ^ { 2 }y=x2

Select the correct graph of the function given by f(x)=x4f ( x ) = x ^ { 4 }f(x)=x4 . Explain how the graph of function g differs (if it does) from the graph of each function fff . g(x)=f(x)+8g ( x ) = f ( x ) + 8g(x)=f(x)+8

Solve the equation and write complex solutions in standard form. x2−10x+41=0x ^ { 2 } - 10 x + 41 = 0x2−10x+41=0

Describe the right-hand and the left-hand behavior of the graph of n(x)=−811(x3−4x2+x+1)n ( x ) = - \frac { 8 } { 11 } \left( x ^ { 3 } - 4 x ^ { 2 } + x + 1 \right)n(x)=−118​(x3−4x2+x+1)

Find vertical asymptotes of the following function. g(x)=x−6x2−36g ( x ) = \frac { x - 6 } { x ^ { 2 } - 36 }g(x)=x2−36x−6​

Functions and Their Graphs

Exponential and Logarithmic Functions

Trigonometry

Analytic Trigonometry

Topics in Analytic Geometry

Filters

Identify all intercepts of $f ( x ) = \frac { x ^ { 2 } } { x ^ { 2 } + 16 }$

Select the graph of the function $y = ( x / 3 ) ^ { 2 } - 5$ . Compare the graph of this function with the graph of $y = x ^ { 2 }$

Select the correct graph of the function given by $f ( x ) = x ^ { 4 }$ . Explain how the graph of function g differs (if it does) from the graph of each function $f$ . $g ( x ) = f ( x ) + 8$

Solve the equation and write complex solutions in standard form. $x ^ { 2 } - 10 x + 41 = 0$

Describe the right-hand and the left-hand behavior of the graph of $n ( x ) = - \frac { 8 } { 11 } \left( x ^ { 3 } - 4 x ^ { 2 } + x + 1 \right)$

Find vertical asymptotes of the following function. $g ( x ) = \frac { x - 6 } { x ^ { 2 } - 36 }$