Question 1

For the pair of functions, perform the indicated operation.
-f(x) = $\frac { 5 x - 8 } { 3 } , g ( x ) = \frac { 1 } { x }$ Find  (f - g)(x) .

Accepted Answer

A)  $\frac { 5 x - 8 } { 3 - x }$ 
B)  $\frac { 5 x ^ { 2 } - 8 x - 3 } { 3 x }$ 
C)  $\frac { 5 x ^ { 2 } - 8 x + 3 } { 3 x }$ 
D)  $\frac { 5 x ^ { 2 } - 8 x - 1 } { 3 x }$ 
A)  $\frac { 5 x - 8 } { 3 - x }$ 
B)  $\frac { 5 x ^ { 2 } - 8 x - 3 } { 3 x }$ 
C)  $\frac { 5 x ^ { 2 } - 8 x + 3 } { 3 x }$ 
D)  $\frac { 5 x ^ { 2 } - 8 x - 1 } { 3 x }$

Question 2

On the day when Julie left for her vacation, the function that converted U.S. dollars to British pounds was  f(x)=   0.54521 x , where  x  is the number of U.S. dollars and  f(x)  is the number of British pounds. Find the inverse function.

Accepted Answer

A)  $f ^ { - 1 } ( x ) = \frac { x } { 0.54521 }$ 
B)  $f ^ { - 1 } ( x ) = x - 0.54521$ 
C)  $\mathrm { f } ^ { - 1 } ( \mathrm { x } ) = \frac { 0.54521 } { \mathrm { x } }$ 
D)  $\mathrm { f } ^ { - 1 } ( \mathrm { x } ) = \frac { 1 } { 0.54521 \mathrm { x } }$ 
A)  $f ^ { - 1 } ( x ) = \frac { x } { 0.54521 }$ 
B)  $f ^ { - 1 } ( x ) = x - 0.54521$ 
C)  $\mathrm { f } ^ { - 1 } ( \mathrm { x } ) = \frac { 0.54521 } { \mathrm { x } }$ 
D)  $\mathrm { f } ^ { - 1 } ( \mathrm { x } ) = \frac { 1 } { 0.54521 \mathrm { x } }$

Question 3

Use the given graph of f(x) $f ( x ) = a x ^ { 2 } + b x + c$ c to solve the specified inequality.
-$f(x) \leq 0$

Accepted Answer

A)  $x \leq 2$ or $x \geq 5$ 
B)  no solution 
C)  $x \leq 2$ 
D)  $2 \leq x \leq 5$ 
A)  $x \leq 2$ or $x \geq 5$ 
B)  no solution 
C)  $x \leq 2$ 
D)  $2 \leq x \leq 5$

Question 4

Provide an appropriate response.
-If the graph of a one-to-one function and its inverse intersect, what is true about any such point of intersection?

Accepted Answer

The x-coordinate and y-coordin

Question 5

For the pair of functions, perform the indicated operation.
-$f ( x ) = 3 x + 8 , g ( x ) = 4 x + 6 \quad$ Find $( f \cdot g ) ( x )$

Accepted Answer

A)  $12 x ^ { 2 } + 50 x + 48$ 
B)  $7 x ^ { 2 } + 50 x + 14$ 
C)  $12 x ^ { 2 } + 48$ 
D)  $12 x ^ { 2 } + 38 x + 48$ 
A)  $12 x ^ { 2 } + 50 x + 48$ 
B)  $7 x ^ { 2 } + 50 x + 14$ 
C)  $12 x ^ { 2 } + 48$ 
D)  $12 x ^ { 2 } + 38 x + 48$

Question 6

Fill in each blank with the appropriate response.
-The graph of $y = - \frac { 1 } { 6 } ( x + 3 ) ^ { 2 } - 8$ can be obtained from the graph of $y = x ^ { 2 }$ by shifting horizontally$\underline{\quad\quad}$ units to the$\underline{\quad\quad}$ vertically compressing by a factor of$\underline{\quad\quad}$ , reflecting across the$\underline{\quad\quad}$ -axis, and shifting vertically$\underline{\quad\quad}$ units in the$\underline{\quad\quad}$ direction.

Accepted Answer

A)  $3 ;$ left; $\frac { 1 } { 6 } ; x ; 8 ;$ downward 
B)  3 ; right; $\frac { 1 } { 6 } ; x ; 8 ;$ downward 
C)  $3 ;$ left; $8 ; x ; \frac { 1 } { 6 } ;$ downward 
D)  3 ; right; $\frac { 1 } { 6 } ; \mathrm { x } ; 8$; upward 
A)  $3 ;$ left; $\frac { 1 } { 6 } ; x ; 8 ;$ downward 
B)  3 ; right; $\frac { 1 } { 6 } ; x ; 8 ;$ downward 
C)  $3 ;$ left; $8 ; x ; \frac { 1 } { 6 } ;$ downward 
D)  3 ; right; $\frac { 1 } { 6 } ; \mathrm { x } ; 8$; upward

Question 7

Solve the inequality.
-$x ^ { 2 } + 6 x \leq - 8$

Accepted Answer

A)  $x \leq 2 \text { or } x \geq 4$ 
B)  $2 < x < 4$ 
C)  $2 \leq x \leq 4$ 
D)  $- 4 \leq x \leq - 2$ 
A)  $x \leq 2 \text { or } x \geq 4$ 
B)  $2 < x < 4$ 
C)  $2 \leq x \leq 4$ 
D)  $- 4 \leq x \leq - 2$

Question 8

Solve the equation
-$\sqrt { x } - \sqrt { 7 x - 7 } = 1$

Accepted Answer

A)   x=-$\frac { 2 } { 9 }$ 
B)   x= $\frac { 16 } { 9 }$ 
C)   x=1 
D)   x= $\frac { 2 } { 9 }$ 
A)   x=-$\frac { 2 } { 9 }$ 
B)   x= $\frac { 16 } { 9 }$ 
C)   x=1 
D)   x= $\frac { 2 } { 9 }$

Question 9

The graphs of two functions f(x) and g(x) are given.
-Solve $f ( x ) \leq g ( x )$.

Accepted Answer

A)  $x \leq - 1$ or $1 \leq x \leq 4$ 
B)  $- 1 \leq x \leq 4$ 
C)  $x \leq 2$ or $1 \leq x \leq 4$ 
D)  $1 \leq x \leq 4$ 
A)  $x \leq - 1$ or $1 \leq x \leq 4$ 
B)  $- 1 \leq x \leq 4$ 
C)  $x \leq 2$ or $1 \leq x \leq 4$ 
D)  $1 \leq x \leq 4$

Question 10

Solve the equation
-$x ^ { 4 } - 5 x ^ { 2 } + 4 = 0$

Accepted Answer

A)   -5.5 
B)   -2,-1,1,2 
C)   -2,2 
D)   -4.4 
A)   -5.5 
B)   -2,-1,1,2 
C)   -2,2 
D)   -4.4

Question 11

Solve the equation
-$\sqrt { 5 x - 9 } + 9 = x$

Accepted Answer

A)   x=9 
B)   x=18, x=5 
C)   x=18 
D)  No solution 
A)   x=9 
B)   x=18, x=5 
C)   x=18 
D)  No solution

Question 12

Find the requested function value.
-Find $( f \circ g ) ( \quad )$ when $f ( x ) = x - 6$ and $g ( x ) = - 8 x ^ { 2 } + 8 x + 3$

Accepted Answer

A)  $- 1191$ 
B)  3 
C)  $- 4413$ 
D)  9 
A)  $- 1191$ 
B)  3 
C)  $- 4413$ 
D)  9

Question 13

Graph the given function as a solid line (or curve) and its inverse as a dashed line (or curve) on the same set of axes.
-$$f ( x ) = 5 x$$

Accepted Answer

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

Question 14

If the following defines a one-to-one function, find its inverse. If not, write "Not one-to-one."
-$$\begin{array}{l}
\begin{array} { c | c } 
x & f ( x ) \
\hline 2 & 24 \
\hline 9 & - 4 \
\hline 13 & - 4 \
\hline 17 & 18
\end{array}\\
\begin{array} { l | l } 
\mathrm { x } & \mathrm { f } ^ { - 1 } ( \mathrm { x } ) \
\hline & \
\hline & \
\hline & \
\hline &
\end{array}
\end{array}$$

Accepted Answer

A) $\begin{array} { c | c } 
\mathrm { x } & \mathrm { f } ^ { - 1 } ( \mathrm { x } ) \
\hline 24 & 2 \
\hline - 4 & 9 \
\hline - 4 & 13 \
\hline 18 & 17
\end{array}$ 
B) $\begin{array} { c | c } 
\mathrm { x } & \mathrm { f } ( \mathrm { x } ) \
\hline 2 & 18 \
\hline 9 & 24 \
\hline 13 & - 4 \
\hline 17 & - 4
\end{array}$ 
C) $\text { Not one-to-one }$ 
D) $\begin{array} { c | c } 
\mathrm { x } & \mathrm { f } ^ { - 1 } ( \mathrm { x } ) \
\hline 24 & 2 \
\hline - 4 & 9 \
\hline - 4 & 17 \
\hline 18 & 13
\end{array}$ 
A) $\begin{array} { c | c } 
\mathrm { x } & \mathrm { f } ^ { - 1 } ( \mathrm { x } ) \
\hline 24 & 2 \
\hline - 4 & 9 \
\hline - 4 & 13 \
\hline 18 & 17
\end{array}$ 
B) $\begin{array} { c | c } 
\mathrm { x } & \mathrm { f } ( \mathrm { x } ) \
\hline 2 & 18 \
\hline 9 & 24 \
\hline 13 & - 4 \
\hline 17 & - 4
\end{array}$ 
C) $\text { Not one-to-one }$ 
D) $\begin{array} { c | c } 
\mathrm { x } & \mathrm { f } ^ { - 1 } ( \mathrm { x } ) \
\hline 24 & 2 \
\hline - 4 & 9 \
\hline - 4 & 17 \
\hline 18 & 13
\end{array}$

Question 15

Ken is 6 feet tall and is walking away from a streetlight. The streetlight has its light bulb 14 feet above the ground, and Ken is walking at the rate of  4.1  feet per second. Find a function,  d(t) , which gives the distance Ken is from the streetlight in terms of time. Find a function,  S(d) , which gives the length of Ken's shadow in terms of d. Then find  S(d) . What is the meaning of $( S \circ d ) ( t )$

Accepted Answer

A)  $( S \circ \mathrm { d } ) ( \mathrm { t } )$ gives the time in terms of Ken's distance from the streetlight. 
B)  $( S \circ d ) ( t )$ gives the distance Ken is from the streetlight in terms of time. 
C)  $( S \circ d ) ( t )$ gives the length of Ken's shadow in terms of time. 
D)  $( \mathrm { S } \circ \mathrm { d } ) ( \mathrm { t } )$ gives the length of Ken's shadow in terms of his distance from the streetlight. 
A)  $( S \circ \mathrm { d } ) ( \mathrm { t } )$ gives the time in terms of Ken's distance from the streetlight. 
B)  $( S \circ d ) ( t )$ gives the distance Ken is from the streetlight in terms of time. 
C)  $( S \circ d ) ( t )$ gives the length of Ken's shadow in terms of time. 
D)  $( \mathrm { S } \circ \mathrm { d } ) ( \mathrm { t } )$ gives the length of Ken's shadow in terms of his distance from the streetlight.

Question 16

The linear equation  y=443 x+3420  provides an approximation of the annual cost (in dollars) of health insurance for a family of three, where  x=1  represents  2011, x=2  represents 2012, and so on. Write an equation that yields the same  y -values when the exact year number is entered.

Accepted Answer

A)   y=443(2010-x)+3420 
B)   y=443(x-2011)+3420 
C)   y=443(x-2010)+3420 
D)   y=443(2011-x)+3420 
A)   y=443(2010-x)+3420 
B)   y=443(x-2011)+3420 
C)   y=443(x-2010)+3420 
D)   y=443(2011-x)+3420

Question 17

For the functions f and g, find the requested value.
-$$\text { Evaluate } ( f + g ) ( 3 )$$

Accepted Answer

A)  3 
B)  $- 1$ 
C)  0 
D)  1 
A)  3 
B)  $- 1$ 
C)  0 
D)  1

Question 18

Determine whether or not the function is one-to-one.
-$f ( x ) = 8 x ^ { 2 } + 1$

Accepted Answer

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

Question 19

Find the requested composition of functions.
-Given $f ( x ) = | 18 - x | \text { and } g ( x ) = 3 x + 2 \text {, find } ( f \circ g ) ( x )$

Accepted Answer

A)  $3 | 18 - x | + 2$ 
B)  $| 20 - 3 x |$ 
C)  $| 16 + 3 x |$ 
D)  $| 16 - 3 x |$ 
A)  $3 | 18 - x | + 2$ 
B)  $| 20 - 3 x |$ 
C)  $| 16 + 3 x |$ 
D)  $| 16 - 3 x |$

Question 20

Solve the inequality.
-$x ^ { 2 } - 3 x \geq 0$

Accepted Answer

A)  $x \leq - 3 \text { or } x \geq 0$ 
B)  $- 3 \leq x \leq 0$ 
C)  $x \leq 0 \text { or } x \geq 3$ 
D)  $0 \leq x \leq 3$ 
A)  $x \leq - 3 \text { or } x \geq 0$ 
B)  $- 3 \leq x \leq 0$ 
C)  $x \leq 0 \text { or } x \geq 3$ 
D)  $0 \leq x \leq 3$

For the pair of functions, perform the indicated operation. -f(x) = $\frac { 5 x - 8 } { 3 } , g ( x ) = \frac { 1 } { x }$ Find (f - g)(x) .

On the day when Julie left for her vacation, the function that converted U.S. dollars to British pounds was f(x)= 0.54521 x , where x is the number of U.S. dollars and f(x) is the number of British pounds. Find the inverse function.

Use the given graph of f(x) $f ( x ) = a x ^ { 2 } + b x + c$ c to solve the specified inequality. - $f(x) \leq 0$ $Use the given graph of f(x) f ( x ) = a x ^ { 2 } + b x + c c to solve the specified inequality. - f(x) \leq 0$

Provide an appropriate response. -If the graph of a one-to-one function and its inverse intersect, what is true about any such point of intersection?

For the pair of functions, perform the indicated operation. - $f ( x ) = 3 x + 8 , g ( x ) = 4 x + 6 \quad$ Find $( f \cdot g ) ( x )$

Solve the inequality. - $x ^ { 2 } + 6 x \leq - 8$

Solve the equation - $\sqrt { x } - \sqrt { 7 x - 7 } = 1$

The graphs of two functions f(x) and g(x) are given. -Solve $f ( x ) \leq g ( x )$ . $The graphs of two functions f(x) and g(x) are given. -Solve f ( x ) \leq g ( x ) .$

Solve the equation - $x ^ { 4 } - 5 x ^ { 2 } + 4 = 0$

Solve the equation - $\sqrt { 5 x - 9 } + 9 = x$

Find the requested function value. -Find $( f \circ g ) ( \quad )$ when $f ( x ) = x - 6$ and $g ( x ) = - 8 x ^ { 2 } + 8 x + 3$

Graph the given function as a solid line (or curve) and its inverse as a dashed line (or curve) on the same set of axes. - $f ( x ) = 5 x$

If the following defines a one-to-one function, find its inverse. If not, write "Not one-to-one." - x f(x) 2 24 9 -4 13 -4 17 18 ()

The linear equation y=443 x+3420 provides an approximation of the annual cost (in dollars) of health insurance for a family of three, where x=1 represents 2011, x=2 represents 2012, and so on. Write an equation that yields the same y -values when the exact year number is entered.

For the functions f and g, find the requested value. - $\text { Evaluate } ( f + g ) ( 3 )$ $For the functions f and g, find the requested value. - \text { Evaluate } ( f + g ) ( 3 )$

Determine whether or not the function is one-to-one. - $f ( x ) = 8 x ^ { 2 } + 1$

Find the requested composition of functions. -Given $f ( x ) = | 18 - x | \text { and } g ( x ) = 3 x + 2 \text {, find } ( f \circ g ) ( x )$

Solve the inequality. - $x ^ { 2 } - 3 x \geq 0$

Functions, Graphs, and Models; Linear Functions

Linear Models, Equations, and Inequalities

Quadratic, Piecewise-Defined, and Power Functions

Exponential and Logarithmic Functions

Higher-Degree Polynomial and Rational Functions

Systems of Equations and Matrices

Special Topics in Algebra

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Exam 4: Additional Topics With Functions

For the pair of functions, perform the indicated operation. -f(x) = 5x−83,g(x)=1x\frac { 5 x - 8 } { 3 } , g ( x ) = \frac { 1 } { x }35x−8​,g(x)=x1​ Find (f - g)(x) .

On the day when Julie left for her vacation, the function that converted U.S. dollars to British pounds was f(x)= 0.54521 x , where x is the number of U.S. dollars and f(x) is the number of British pounds. Find the inverse function.

Use the given graph of f(x) f(x)=ax2+bx+cf ( x ) = a x ^ { 2 } + b x + cf(x)=ax2+bx+c c to solve the specified inequality. - f(x)≤0f(x) \leq 0f(x)≤0

Provide an appropriate response. -If the graph of a one-to-one function and its inverse intersect, what is true about any such point of intersection?

For the pair of functions, perform the indicated operation. - f(x)=3x+8,g(x)=4x+6f ( x ) = 3 x + 8 , g ( x ) = 4 x + 6 \quadf(x)=3x+8,g(x)=4x+6 Find (f⋅g)(x)( f \cdot g ) ( x )(f⋅g)(x)

Solve the inequality. - x2+6x≤−8x ^ { 2 } + 6 x \leq - 8x2+6x≤−8

Solve the equation - x−7x−7=1\sqrt { x } - \sqrt { 7 x - 7 } = 1x​−7x−7​=1

The graphs of two functions f(x) and g(x) are given. -Solve f(x)≤g(x)f ( x ) \leq g ( x )f(x)≤g(x) .

Solve the equation - x4−5x2+4=0x ^ { 4 } - 5 x ^ { 2 } + 4 = 0x4−5x2+4=0

Solve the equation - 5x−9+9=x\sqrt { 5 x - 9 } + 9 = x5x−9​+9=x

Find the requested function value. -Find (f∘g)()( f \circ g ) ( \quad )(f∘g)() when f(x)=x−6f ( x ) = x - 6f(x)=x−6 and g(x)=−8x2+8x+3g ( x ) = - 8 x ^ { 2 } + 8 x + 3g(x)=−8x2+8x+3

Graph the given function as a solid line (or curve) and its inverse as a dashed line (or curve) on the same set of axes. - f(x)=5xf ( x ) = 5 xf(x)=5x