Question 1

Determine whether or not the function $f ( x ) = x ^ { 2 } - 3 x + 2$ is one-to-one.

Accepted Answer

$f ( x ) = x ^ { 2 } - 3 x + 2 = ( x - 2 ) ( x - 1 )$ , so $f ( 2 ) = 0 = f ( 1 )$ , so $f$ is not one-to-one.

Question 2

Find the domain of the function $f ( x ) = \frac { x + 1 } { x ^ { 2 } + 1 }$ .

Accepted Answer

There is no value of $x$ that makes the denominator $0$ , thus the domain is all real numbers $( - \infty , \infty )$ .

Question 3

A man is running around a circular track that is 200 m in circumference. An observer uses a stopwatch to record the runner's time at the end of each lap, obtaining the data in the following table.
What was the man's average speed (rate) between 68 s and 203 s? Round the answer to two decimal places.
$$\begin{array} { | c | c | } 
\hline \text { Time (s) } & \begin{array} { c } 
\text { Distance } \
( \mathrm { m } )
\end{array} \
\hline 32 & 200 \
\hline 68 & 400 \
\hline 108 & 600 \
\hline 152 & 800 \
\hline 203 & 1000 \
\hline 263 & 1200 \
\hline 335 & 1400 \
\hline 412 & 1600 \
\hline
\end{array}$$

Accepted Answer

4.44 m/s

Question 4

Let $f ( x ) = x + c$ . Graph the family of functions with $c = - 1$ , $0$ , and $- 1$ in the viewing rectangle $[ - 3,3 ]$ by $[ - 3,3 ]$ . How does the value of $c$ affect the graph?

Accepted Answer

@#IMG-DLM& For values of @#LAT-DLM& the graph of t

Question 5

Sketch the graph of the function $f ( x ) = 2 - | x - 1 |$ , not by plotting points, but by starting with the graph of a standard function and applying transformations.

Accepted Answer

Shift @#LAT-DLM& one unit to t

Question 6

For the function $f ( t ) = \frac { 2 } { t } - 2$ determine the average rate of change between the values $t = a$ and $t = a + h$ .

Accepted Answer

Average ra

Question 7

A function is given. Use a graphing calculator to draw the graph of f. Find the domain and range of f from the graph. $f ( x ) = - \sqrt { 16 - x ^ { 2 } }$

Accepted Answer

The answer of A function is given. Use a graphing...

Question 8

Use the Property of Inverse Functions to show that $f ( x ) = \sqrt { 25 - x ^ { 2 } }$ , $0 \leq x \leq 5$ and $g ( x ) = \sqrt { 25 - x ^ { 2 } }$ , $0 \leq x \leq 5$ are inverses of each other.

Accepted Answer

The answer of Use the Property of Inverse Functions to...

Question 9

The cost $c$ in dollars to manufacture $x$ integrated circuits is given by the function $C ( x ) = 11834 + 0.3 x + 4.56 x ^ { 3 }$ , where $x$ is measured in hundreds. 
(a) Find $C ( 0.05 )$ and $C ( 5 )$ . 
(b) What do the answers in part (a) represent?

Accepted Answer

(a) @#LAT-DLM&, 834 ,@#LAT-DLM& , 406
(b) It costs

Question 10

Use a graphing device to draw the graph of the function $f ( x ) = 144 x ^ { 3 } - 144 x ^ { 2 } + 36 x$ . State approximately the intervals on which the function is increasing and on which the function is decreasing.

Accepted Answer

@#LAT-DLM& is increa

Question 11

If $f ( x ) = - 4 x + 3$ , find $f ( - 3 )$ , $f ( - 1 )$ , $f ( 2 )$ .

Accepted Answer

The answer of If \(f ( x ) = -...

Question 12

Determine whether $f ( x ) = 5 x ^ { 2 } - \frac { x ^ { 4 } } { 5 }$ is even or odd. If $f$ is even or odd, use symmetry to sketch its graph.

Accepted Answer

@#LAT-DLM& . So @#LAT-DLM& , a

Question 13

If $h ( t ) = t - 2 / t$ , find $h ( - 2 )$ , $h ( 1 )$ , $h ( 2 )$ .

Accepted Answer

The answer of If \(h ( t ) = t...

Question 14

Use $f ( x ) = x - 3$ and $g ( x ) = 3 + x ^ { 2 }$ to evaluate the expression $( g \circ f ) ( - 1 )$ .

Accepted Answer

A)  $14$ 
B)  $19$ 
C)  $3$ 
D)  $12$ 
E)  $- 12$ 
A)  $14$ 
B)  $19$ 
C)  $3$ 
D)  $12$ 
E)  $- 12$

Question 15

Explain how the graph of $g ( x ) = \frac { | x + 1 | - 2 } { 3 }$ is obtained from the graph of $f = | x |$ .

Accepted Answer

A)  Shift the graph of $f$ one unit to the right, then shift downward
$\frac { 2 } { 3 }$ units. 
B)  Shift the graph of $f$ one unit to the right, then shift downward
$2$ units. 
C)  Shift the graph of $f$ one unit to the left, then shrink vertically by a factor of
$\frac { 2 } { 3 }$ . 
D)  Shift the graph of $f$ one unit to the left, then shift upward
$\frac { 2 } { 3 }$ units. 
E)  Shift the graph of $f$ one unit to the left, shrink vertically by a factor of
$\frac { 1 } { 3 }$ , shift downward
$\frac { 2 } { 3 }$ units. 
A)  Shift the graph of $f$ one unit to the right, then shift downward
$\frac { 2 } { 3 }$ units. 
B)  Shift the graph of $f$ one unit to the right, then shift downward
$2$ units. 
C)  Shift the graph of $f$ one unit to the left, then shrink vertically by a factor of
$\frac { 2 } { 3 }$ . 
D)  Shift the graph of $f$ one unit to the left, then shift upward
$\frac { 2 } { 3 }$ units. 
E)  Shift the graph of $f$ one unit to the left, shrink vertically by a factor of
$\frac { 1 } { 3 }$ , shift downward
$\frac { 2 } { 3 }$ units.

Question 16

For the function $f ( x ) = 2 x ^ { 2 } - x$ determine the average rate of change between the values $x = - 1$ and $x = 0 .$

Accepted Answer

Average ra

Question 17

Express the rule in function notation.
Square, subtract $5$ , then take the square root.

Accepted Answer

A) 
 $f ( x ) = \sqrt { x ^ { 2 } - 5 }$ 
B) 
 $f ( x ) = x - \sqrt { 5 }$ 
C) 
 $f ( x ) = x ^ { 2 } - 5$ 
D) 
 $f ( x ) = \sqrt { 5 x ^ { 2 } }$ 
E) 
 $f ( x ) = \sqrt { - 5 x ^ { 2 } }$ 
A) 
 $f ( x ) = \sqrt { x ^ { 2 } - 5 }$ 
B) 
 $f ( x ) = x - \sqrt { 5 }$ 
C) 
 $f ( x ) = x ^ { 2 } - 5$ 
D) 
 $f ( x ) = \sqrt { 5 x ^ { 2 } }$ 
E) 
 $f ( x ) = \sqrt { - 5 x ^ { 2 } }$

Question 18

Use a graphing device to draw the graph of the function $f ( x ) = x ^ { 5 } - 6 x ^ { 4 } + 11 x ^ { 3 } - 6 x ^ { 2 }$ . State approximately the intervals on which the function is increasing and on which the function is decreasing.

Accepted Answer

@#LAT-DLM& is increasing on @#LAT-DLM& ,

Question 19

For the function $f ( x ) = 4 + \frac { 1 } { 2 } x$ determine the average rate of change between the values $x = 0$ and $x = 6$ .

Accepted Answer

Average ra

Question 20

Given the graph of $f$ , describe how the graph of $y = - f ( 2 x ) + 2$ can be obtained from the graph of $f$

Accepted Answer

A)  Stretch horizontally by a factor of $2$ , then reflecting about the
$y$ - axis, then shifting
$2$ units up 
B)  Shrink vertically by a factor of $2$ , then reflecting about the
$x$ - axis, then shifting
$2$ units up. 
C)  Stretch horizontally by a factor of $2$ , then reflecting about the
$y$ - axis, then shifting
$2$ units up . 
D)  Shrink vertically by a factor of $\frac { 1 } { 2 }$ , then reflecting about the
$x$ - axis, then shifting downward
$2$ units. 
E)  Shrink horizontally by a factor of $\frac { 1 } { 2 }$ , then reflecting about the
$x$ - axis, then shifting
$2$ units up 
A)  Stretch horizontally by a factor of $2$ , then reflecting about the
$y$ - axis, then shifting
$2$ units up 
B)  Shrink vertically by a factor of $2$ , then reflecting about the
$x$ - axis, then shifting
$2$ units up. 
C)  Stretch horizontally by a factor of $2$ , then reflecting about the
$y$ - axis, then shifting
$2$ units up . 
D)  Shrink vertically by a factor of $\frac { 1 } { 2 }$ , then reflecting about the
$x$ - axis, then shifting downward
$2$ units. 
E)  Shrink horizontally by a factor of $\frac { 1 } { 2 }$ , then reflecting about the
$x$ - axis, then shifting
$2$ units up

Determine whether or not the function $f ( x ) = x ^ { 2 } - 3 x + 2$ is one-to-one.

Find the domain of the function $f ( x ) = \frac { x + 1 } { x ^ { 2 } + 1 }$ .

Let $f ( x ) = x + c$ . Graph the family of functions with $c = - 1$ , $0$ , and $- 1$ in the viewing rectangle $[ - 3,3 ]$ by $[ - 3,3 ]$ . How does the value of $c$ affect the graph?

Sketch the graph of the function $f ( x ) = 2 - | x - 1 |$ , not by plotting points, but by starting with the graph of a standard function and applying transformations.

For the function $f ( t ) = \frac { 2 } { t } - 2$ determine the average rate of change between the values $t = a$ and $t = a + h$ .

A function is given. Use a graphing calculator to draw the graph of f. Find the domain and range of f from the graph. $f ( x ) = - \sqrt { 16 - x ^ { 2 } }$

Use the Property of Inverse Functions to show that $f ( x ) = \sqrt { 25 - x ^ { 2 } }$ , $0 \leq x \leq 5$ and $g ( x ) = \sqrt { 25 - x ^ { 2 } }$ , $0 \leq x \leq 5$ are inverses of each other.

The cost $c$ in dollars to manufacture $x$ integrated circuits is given by the function $C ( x ) = 11834 + 0.3 x + 4.56 x ^ { 3 }$ , where $x$ is measured in hundreds. (a) Find $C ( 0.05 )$ and $C ( 5 )$ . (b) What do the answers in part (a) represent?

Use a graphing device to draw the graph of the function $f ( x ) = 144 x ^ { 3 } - 144 x ^ { 2 } + 36 x$ . State approximately the intervals on which the function is increasing and on which the function is decreasing.

If $f ( x ) = - 4 x + 3$ , find $f ( - 3 )$ , $f ( - 1 )$ , $f ( 2 )$ .

Determine whether $f ( x ) = 5 x ^ { 2 } - \frac { x ^ { 4 } } { 5 }$ is even or odd. If $f$ is even or odd, use symmetry to sketch its graph.

If $h ( t ) = t - 2 / t$ , find $h ( - 2 )$ , $h ( 1 )$ , $h ( 2 )$ .

Use $f ( x ) = x - 3$ and $g ( x ) = 3 + x ^ { 2 }$ to evaluate the expression $( g \circ f ) ( - 1 )$ .

Explain how the graph of $g ( x ) = \frac { | x + 1 | - 2 } { 3 }$ is obtained from the graph of $f = | x |$ .

For the function $f ( x ) = 2 x ^ { 2 } - x$ determine the average rate of change between the values $x = - 1$ and $x = 0 .$

Express the rule in function notation. Square, subtract $5$ , then take the square root.

Use a graphing device to draw the graph of the function $f ( x ) = x ^ { 5 } - 6 x ^ { 4 } + 11 x ^ { 3 } - 6 x ^ { 2 }$ . State approximately the intervals on which the function is increasing and on which the function is decreasing.

For the function $f ( x ) = 4 + \frac { 1 } { 2 } x$ determine the average rate of change between the values $x = 0$ and $x = 6$ .

Given the graph of $f$ , describe how the graph of $y = - f ( 2 x ) + 2$ can be obtained from the graph of $f$

Fundamentals

Polynomial and Rational Functions

Exponential and Logarithmic Functions

Trigonometric Functions: Unit Circle Approach

Trigonometric Functions: Right Triangle Approach

Analytic Trigonometry

Polar Coordinates and Parametric Equations

Vectors in Two and Three Dimensions

Systems of Equations and Inequalities

Conic Sections

Sequences and Series

Limits: a Preview of Calculus

Filters

Exam 2: Functions

Determine whether or not the function f(x)=x2−3x+2f ( x ) = x ^ { 2 } - 3 x + 2f(x)=x2−3x+2 is one-to-one.

Find the domain of the function f(x)=x+1x2+1f ( x ) = \frac { x + 1 } { x ^ { 2 } + 1 }f(x)=x2+1x+1​ .

Let f(x)=x+cf ( x ) = x + cf(x)=x+c . Graph the family of functions with c=−1c = - 1c=−1 , 000 , and −1- 1−1 in the viewing rectangle [−3,3][ - 3,3 ][−3,3] by [−3,3][ - 3,3 ][−3,3] . How does the value of ccc affect the graph?

Sketch the graph of the function f(x)=2−∣x−1∣f ( x ) = 2 - | x - 1 |f(x)=2−∣x−1∣ , not by plotting points, but by starting with the graph of a standard function and applying transformations.

For the function f(t)=2t−2f ( t ) = \frac { 2 } { t } - 2f(t)=t2​−2 determine the average rate of change between the values t=at = at=a and t=a+ht = a + ht=a+h .

A function is given. Use a graphing calculator to draw the graph of f. Find the domain and range of f from the graph. f(x)=−16−x2f ( x ) = - \sqrt { 16 - x ^ { 2 } }f(x)=−16−x2​

Use the Property of Inverse Functions to show that f(x)=25−x2f ( x ) = \sqrt { 25 - x ^ { 2 } }f(x)=25−x2​ , 0≤x≤50 \leq x \leq 50≤x≤5 and g(x)=25−x2g ( x ) = \sqrt { 25 - x ^ { 2 } }g(x)=25−x2​ , 0≤x≤50 \leq x \leq 50≤x≤5 are inverses of each other.

Use a graphing device to draw the graph of the function f(x)=144x3−144x2+36xf ( x ) = 144 x ^ { 3 } - 144 x ^ { 2 } + 36 xf(x)=144x3−144x2+36x . State approximately the intervals on which the function is increasing and on which the function is decreasing.

If f(x)=−4x+3f ( x ) = - 4 x + 3f(x)=−4x+3 , find f(−3)f ( - 3 )f(−3) , f(−1)f ( - 1 )f(−1) , f(2)f ( 2 )f(2) .

Determine whether f(x)=5x2−x45f ( x ) = 5 x ^ { 2 } - \frac { x ^ { 4 } } { 5 }f(x)=5x2−5x4​ is even or odd. If fff is even or odd, use symmetry to sketch its graph.

If h(t)=t−2/th ( t ) = t - 2 / th(t)=t−2/t , find h(−2)h ( - 2 )h(−2) , h(1)h ( 1 )h(1) , h(2)h ( 2 )h(2) .

Use f(x)=x−3f ( x ) = x - 3f(x)=x−3 and g(x)=3+x2g ( x ) = 3 + x ^ { 2 }g(x)=3+x2 to evaluate the expression (g∘f)(−1)( g \circ f ) ( - 1 )(g∘f)(−1) .

Explain how the graph of g(x)=∣x+1∣−23g ( x ) = \frac { | x + 1 | - 2 } { 3 }g(x)=3∣x+1∣−2​ is obtained from the graph of f=∣x∣f = | x |f=∣x∣ .

For the function f(x)=2x2−xf ( x ) = 2 x ^ { 2 } - xf(x)=2x2−x determine the average rate of change between the values x=−1x = - 1x=−1 and x=0.x = 0 .x=0.

Express the rule in function notation. Square, subtract 555 , then take the square root.

Use a graphing device to draw the graph of the function f(x)=x5−6x4+11x3−6x2f ( x ) = x ^ { 5 } - 6 x ^ { 4 } + 11 x ^ { 3 } - 6 x ^ { 2 }f(x)=x5−6x4+11x3−6x2 . State approximately the intervals on which the function is increasing and on which the function is decreasing.

For the function f(x)=4+12xf ( x ) = 4 + \frac { 1 } { 2 } xf(x)=4+21​x determine the average rate of change between the values x=0x = 0x=0 and x=6x = 6x=6 .

Given the graph of fff , describe how the graph of y=−f(2x)+2y = - f ( 2 x ) + 2y=−f(2x)+2 can be obtained from the graph of fff

Fundamentals

Polynomial and Rational Functions

Exponential and Logarithmic Functions

Trigonometric Functions: Unit Circle Approach

Trigonometric Functions: Right Triangle Approach

Analytic Trigonometry

Polar Coordinates and Parametric Equations

Vectors in Two and Three Dimensions

Systems of Equations and Inequalities

Conic Sections

Sequences and Series

Limits: a Preview of Calculus

Filters

Determine whether or not the function $f ( x ) = x ^ { 2 } - 3 x + 2$ is one-to-one.

Find the domain of the function $f ( x ) = \frac { x + 1 } { x ^ { 2 } + 1 }$ .

Let $f ( x ) = x + c$ . Graph the family of functions with $c = - 1$ , $0$ , and $- 1$ in the viewing rectangle $[ - 3,3 ]$ by $[ - 3,3 ]$ . How does the value of $c$ affect the graph?

Sketch the graph of the function $f ( x ) = 2 - | x - 1 |$ , not by plotting points, but by starting with the graph of a standard function and applying transformations.

For the function $f ( t ) = \frac { 2 } { t } - 2$ determine the average rate of change between the values $t = a$ and $t = a + h$ .

A function is given. Use a graphing calculator to draw the graph of f. Find the domain and range of f from the graph. $f ( x ) = - \sqrt { 16 - x ^ { 2 } }$

Use the Property of Inverse Functions to show that $f ( x ) = \sqrt { 25 - x ^ { 2 } }$ , $0 \leq x \leq 5$ and $g ( x ) = \sqrt { 25 - x ^ { 2 } }$ , $0 \leq x \leq 5$ are inverses of each other.

Use a graphing device to draw the graph of the function $f ( x ) = 144 x ^ { 3 } - 144 x ^ { 2 } + 36 x$ . State approximately the intervals on which the function is increasing and on which the function is decreasing.

If $f ( x ) = - 4 x + 3$ , find $f ( - 3 )$ , $f ( - 1 )$ , $f ( 2 )$ .

Determine whether $f ( x ) = 5 x ^ { 2 } - \frac { x ^ { 4 } } { 5 }$ is even or odd. If $f$ is even or odd, use symmetry to sketch its graph.

If $h ( t ) = t - 2 / t$ , find $h ( - 2 )$ , $h ( 1 )$ , $h ( 2 )$ .

Use $f ( x ) = x - 3$ and $g ( x ) = 3 + x ^ { 2 }$ to evaluate the expression $( g \circ f ) ( - 1 )$ .

Explain how the graph of $g ( x ) = \frac { | x + 1 | - 2 } { 3 }$ is obtained from the graph of $f = | x |$ .

For the function $f ( x ) = 2 x ^ { 2 } - x$ determine the average rate of change between the values $x = - 1$ and $x = 0 .$

Express the rule in function notation. Square, subtract $5$ , then take the square root.

Use a graphing device to draw the graph of the function $f ( x ) = x ^ { 5 } - 6 x ^ { 4 } + 11 x ^ { 3 } - 6 x ^ { 2 }$ . State approximately the intervals on which the function is increasing and on which the function is decreasing.

For the function $f ( x ) = 4 + \frac { 1 } { 2 } x$ determine the average rate of change between the values $x = 0$ and $x = 6$ .

Given the graph of $f$ , describe how the graph of $y = - f ( 2 x ) + 2$ can be obtained from the graph of $f$