Question 1

Given $f ( x ) = \frac { x ^ { 2 } + x - 2 } { x - 1 }$ , find a linear function $g$ which is identical to $f$

Accepted Answer

The answer of Given \(f ( x ) = \frac...

Question 2

Find the domain and range of the piecewise defined function:   $$f ( x ) = \left\{ \begin{array} { c c } 
- 1 & x \leq - 5 \
\frac { 1 } { x } & - 5  5
\end{array} \right.$$

Accepted Answer

A)  Domain: $( - \infty , \infty )$ Range: $( - \infty , \infty )$ 
B)  Domain: $( - \infty , 5 ) \cup ( 5 , \infty )$ Range: $( - \infty , \infty )$ 
C)  Domain: $( - \infty , 0 ) \cup ( 0,5 ) \cup ( 5 , \infty )$ Range: $[ 0 , \infty )$ 
D)  Domain: $( - \infty , 0 ) \cup ( 0,5 ) \cup ( 5 , \infty )$ Range: $\{ - 1 \} \cup [ 0 , \infty )$ 
A)  Domain: $( - \infty , \infty )$ Range: $( - \infty , \infty )$ 
B)  Domain: $( - \infty , 5 ) \cup ( 5 , \infty )$ Range: $( - \infty , \infty )$ 
C)  Domain: $( - \infty , 0 ) \cup ( 0,5 ) \cup ( 5 , \infty )$ Range: $[ 0 , \infty )$ 
D)  Domain: $( - \infty , 0 ) \cup ( 0,5 ) \cup ( 5 , \infty )$ Range: $\{ - 1 \} \cup [ 0 , \infty )$

Question 3

(-3, 4) is on the graph of an odd function $f ( x )$ find another point on the graph of $f ( x )$

Accepted Answer

A)  (-3, 3) 
B)  (-3, 4) 
C)  (3, 4) 
D)  (3, -4) 
A)  (-3, 3) 
B)  (-3, 4) 
C)  (3, 4) 
D)  (3, -4)

Question 4

Given $y = x ^ { 2 } - 4 x - 8$ , for what value(s) of $X$ is $y = - 3$ ?

Accepted Answer

A)  -5 and 1 
B)  5 and 1 
C)  4 and 2 
D)  -1 and 5 
A)  -5 and 1 
B)  5 and 1 
C)  4 and 2 
D)  -1 and 5

Question 5

Find the domain of $f ( x ) = \frac { x ^ { 2 } - 9 } { \sqrt { x + 3 } }$

Accepted Answer

A)  Domain: $[ - 3 , \infty )$ 
B)  Domain: $( - 3 , \infty )$ 
C)  Domain: $( - \infty , \infty )$ 
D)  Domain: $( - \infty , - 3 ) \cup ( - 3 , \infty )$ 
A)  Domain: $[ - 3 , \infty )$ 
B)  Domain: $( - 3 , \infty )$ 
C)  Domain: $( - \infty , \infty )$ 
D)  Domain: $( - \infty , - 3 ) \cup ( - 3 , \infty )$

Question 6

Find the equation of a linear function whose graph passes through the points (2, -1) and (-3, 2).

Accepted Answer

A)  $5 x + 3 y + 7 = 0$ 
B)  $5 x + 3 y + 3 = 0$ 
C)  $3 x + 5 y + 3 = 0$ 
D)  $3 x + 5 y + 7 = 0$ 
A)  $5 x + 3 y + 7 = 0$ 
B)  $5 x + 3 y + 3 = 0$ 
C)  $3 x + 5 y + 3 = 0$ 
D)  $3 x + 5 y + 7 = 0$

Question 7

Table below defines two functions $f$ and $g$ Create an additional row for the table for the function $( f \circ g ) ( x )$ 
 $$\begin{array} { | l | l | l | l | l | l | l | l | } 
\hline x & 0 & 1 & 2 & 3 & 4 & 5 & 6 \
\hline f ( x ) & 0 & 1 & 3 & 2 & 3 & 0 & 2 \
\hline g ( x ) & 1 & 0 & 1 & 1 & 0 & 1 & 0 \
\hline
\end{array}$$

Accepted Answer

\[\begin{array} { | l | l | l

Question 8

Write $f ( x ) = \left| 4 - x ^ { 2 } \right|$ as a piecewise function.

Accepted Answer

A)  $f ( x ) = \left\{ \begin{array} { l } 
4 + x ^ { 2 } - 2 \leq x \leq 2 \
4 - x ^ { 2 } \text { otherwise }
\end{array} \right.$ 
B)  $f ( x ) = \left\{ \begin{array} { c c } 
- 4 + x ^ { 2 } & - 2 \leq x \leq 2 \
4 - x ^ { 2 } & \text { otherwise }
\end{array} \right.$ 
C)  $f ( x ) = \left\{ \begin{array} { c c } 
4 + x ^ { 2 } & - 2 \leq x \leq 2 \
- 4 + x ^ { 2 } & \text { otherwise }
\end{array} \right.$ 
D)  $f ( x ) = \left\{ \begin{array} { c c } 
4 - x ^ { 2 } & - 2 \leq x \leq 2 \
- 4 + x ^ { 2 } & \text { otherwise }
\end{array} \right.$ 
A)  $f ( x ) = \left\{ \begin{array} { l } 
4 + x ^ { 2 } - 2 \leq x \leq 2 \
4 - x ^ { 2 } \text { otherwise }
\end{array} \right.$ 
B)  $f ( x ) = \left\{ \begin{array} { c c } 
- 4 + x ^ { 2 } & - 2 \leq x \leq 2 \
4 - x ^ { 2 } & \text { otherwise }
\end{array} \right.$ 
C)  $f ( x ) = \left\{ \begin{array} { c c } 
4 + x ^ { 2 } & - 2 \leq x \leq 2 \
- 4 + x ^ { 2 } & \text { otherwise }
\end{array} \right.$ 
D)  $f ( x ) = \left\{ \begin{array} { c c } 
4 - x ^ { 2 } & - 2 \leq x \leq 2 \
- 4 + x ^ { 2 } & \text { otherwise }
\end{array} \right.$

Question 9

Find the domain and range of $f ( x ) = \frac { \sqrt { 9 - x ^ { 2 } } } { x + 3 }$

Accepted Answer

A)  Domain: [-3, 3] Range: $[ 0 , \infty )$ 
B)  Domain: (-3, 3) Range: $[ 0 , \infty )$ 
C)  Domain: (-3, 3] Range: $[ 0 , \infty )$ 
D)  Domain: (-3, 3] Range: $( 0 , \infty )$ 
A)  Domain: [-3, 3] Range: $[ 0 , \infty )$ 
B)  Domain: (-3, 3) Range: $[ 0 , \infty )$ 
C)  Domain: (-3, 3] Range: $[ 0 , \infty )$ 
D)  Domain: (-3, 3] Range: $( 0 , \infty )$

Question 10

Which of the following points lie on the graph of $$f ( x ) = \sqrt { 3 x + 4 }$$ ?A (-3, 6) B (4, 4) C (0, 4)

Accepted Answer

A)  A and B 
B)  B and C 
C)  Only B 
D)  Only C 
A)  A and B 
B)  B and C 
C)  Only B 
D)  Only C

Question 11

Is $f ( x ) = \frac { 2 x ^ { 3 } } { x ^ { 2 } + 2 }$ an even function, an odd function or neither? Explain.

Accepted Answer

The answer of Is \(f ( x ) = \frac...

Question 12

Solve the following equation for t, on the interval $[ 0 , \pi ]$ : $2 \cos 2 t = \sqrt { 2 }$

Accepted Answer

The answer of Solve the following equation for t, on...

Question 13

Write the following expression as an algebraic expression that does not involve trigonometric or inverse trigonometric functions $\cos \left( 2 \cos ^ { - 1 } 5 x \right)$

Accepted Answer

A)  $1 - 25 x ^ { 2 }$ 
B)  $1 - 50 x ^ { 2 }$ 
C)  $1 + 50 x ^ { 2 }$ 
D)  $50 x ^ { 2 } - 1$ 
A)  $1 - 25 x ^ { 2 }$ 
B)  $1 - 50 x ^ { 2 }$ 
C)  $1 + 50 x ^ { 2 }$ 
D)  $50 x ^ { 2 } - 1$

Question 14

Write all the transformations applied to obtain the graph of $y = | 2 x + 4 | - 3$ from the graph of $y = | x |$

Accepted Answer

Graph of @#LAT-DLM& is shifted left 2 un

Question 15

Write the following expression as an algebraic expression that does not involve trigonometric or inverse trigonometric functions $\tan ^ { 2 } \left( \sec ^ { - 1 } x \right)$

Accepted Answer

The answer of Write the following expression as an algebraic...

Question 16

Write $f ( x ) = 5 + | 3 x - 2 |$ as a piecewise function.

Accepted Answer

A)  $f ( x ) = \left\{ \begin{array} { c c } 
- 3 + 3 x & x < 2 / 3 \
3 - 3 x & x \geq 3 / 2
\end{array} \right.$ 
B)  $f ( x ) = \left\{ \begin{array} { c c } 
- 3 - 3 x & x < 2 / 3 \
3 + 3 x & x \geq 2 / 3
\end{array} \right.$ 
C)  $f ( x ) = \left\{ \begin{array} { l l } 
7 - 3 x & x < 2 / 3 \
3 + 3 x & x \geq 2 / 3
\end{array} \right.$ 
D)  $f ( x ) = \left\{ \begin{array} { l l } 
7 + 3 x & x < 2 / 3 \
3 - 3 x & x \geq 2 / 3
\end{array} \right.$ 
A)  $f ( x ) = \left\{ \begin{array} { c c } 
- 3 + 3 x & x < 2 / 3 \
3 - 3 x & x \geq 3 / 2
\end{array} \right.$ 
B)  $f ( x ) = \left\{ \begin{array} { c c } 
- 3 - 3 x & x < 2 / 3 \
3 + 3 x & x \geq 2 / 3
\end{array} \right.$ 
C)  $f ( x ) = \left\{ \begin{array} { l l } 
7 - 3 x & x < 2 / 3 \
3 + 3 x & x \geq 2 / 3
\end{array} \right.$ 
D)  $f ( x ) = \left\{ \begin{array} { l l } 
7 + 3 x & x < 2 / 3 \
3 - 3 x & x \geq 2 / 3
\end{array} \right.$

Question 17

Find an equation for a polynomial function whose graph passes through the points (3, 0), (-1, 0) and (-3, 0).

Accepted Answer

A)  $f ( x ) = x ^ { 3 } - x ^ { 2 } - 9 x - 9$ 
B)  $f ( x ) = x ^ { 3 } - x ^ { 2 } + 9 x + 9$ 
C)  $f ( x ) = x ^ { 3 } - x ^ { 2 } + 9 x - 9$ 
D)  $f ( x ) = x ^ { 3 } + x ^ { 2 } - 9 x - 9$ 
A)  $f ( x ) = x ^ { 3 } - x ^ { 2 } - 9 x - 9$ 
B)  $f ( x ) = x ^ { 3 } - x ^ { 2 } + 9 x + 9$ 
C)  $f ( x ) = x ^ { 3 } - x ^ { 2 } + 9 x - 9$ 
D)  $f ( x ) = x ^ { 3 } + x ^ { 2 } - 9 x - 9$

Question 18

For the polynomial $f ( x ) = x ^ { 3 } ( 3 - x ) ^ { 2 } \left( 1 + x ^ { 2 } \right)$ , determine the leading coefficient and the degree.

Accepted Answer

A)  $x ^ { 7 } , 3$ 
B)  $x ^ { 7 } , 1$ 
C)  $- x ^ { 7 } , 3$ 
D)  $- x ^ { 7 } , 1$ 
A)  $x ^ { 7 } , 3$ 
B)  $x ^ { 7 } , 1$ 
C)  $- x ^ { 7 } , 3$ 
D)  $- x ^ { 7 } , 1$

Question 19

Write all the transformations applied to obtain the graph of $y = 2 - \sqrt { x + 1 }$ from the graph of $y = \sqrt { x }$

Accepted Answer

Graph of @#LAT-DLM& is shifted left 1 un

Question 20

Given $g ( x ) = \left\{ \begin{array} { c c } 
3 & x < 1 \
\sqrt { x + 1 } & x \geq 1
\end{array} \right.$ Find $g \left( t ^ { 2 } - 1 \right)$

Accepted Answer

None

Given $f ( x ) = \frac { x ^ { 2 } + x - 2 } { x - 1 }$ , find a linear function $g$ which is identical to $f$

Find the domain and range of the piecewise defined function: $f ( x ) = \left\{ \begin{array} { c c } - 1 & x \leq - 5 \\\frac { 1 } { x } & - 5 < x < 5 \\x - 5 & x > 5\end{array} \right.$

(-3, 4) is on the graph of an odd function $f ( x )$ find another point on the graph of $f ( x )$

Given $y = x ^ { 2 } - 4 x - 8$ , for what value(s) of $X$ is $y = - 3$ ?

Find the domain of $f ( x ) = \frac { x ^ { 2 } - 9 } { \sqrt { x + 3 } }$

Find the equation of a linear function whose graph passes through the points (2, -1) and (-3, 2).

Table below defines two functions $f$ and $g$ Create an additional row for the table for the function $( f \circ g ) ( x )$ x 0 1 2 3 4 5 6 f(x) 0 1 3 2 3 0 2 g(x) 1 0 1 1 0 1 0

Write $f ( x ) = \left| 4 - x ^ { 2 } \right|$ as a piecewise function.

Find the domain and range of $f ( x ) = \frac { \sqrt { 9 - x ^ { 2 } } } { x + 3 }$

Which of the following points lie on the graph of $f ( x ) = \sqrt { 3 x + 4 }$ ?A (-3, 6) B (4, 4) C (0, 4)

Is $f ( x ) = \frac { 2 x ^ { 3 } } { x ^ { 2 } + 2 }$ an even function, an odd function or neither? Explain.

Solve the following equation for t, on the interval $[ 0 , \pi ]$ : $2 \cos 2 t = \sqrt { 2 }$

Write the following expression as an algebraic expression that does not involve trigonometric or inverse trigonometric functions $\cos \left( 2 \cos ^ { - 1 } 5 x \right)$

Write all the transformations applied to obtain the graph of $y = | 2 x + 4 | - 3$ from the graph of $y = | x |$

Write the following expression as an algebraic expression that does not involve trigonometric or inverse trigonometric functions $\tan ^ { 2 } \left( \sec ^ { - 1 } x \right)$

Write $f ( x ) = 5 + | 3 x - 2 |$ as a piecewise function.

Find an equation for a polynomial function whose graph passes through the points (3, 0), (-1, 0) and (-3, 0).

For the polynomial $f ( x ) = x ^ { 3 } ( 3 - x ) ^ { 2 } \left( 1 + x ^ { 2 } \right)$ , determine the leading coefficient and the degree.

Write all the transformations applied to obtain the graph of $y = 2 - \sqrt { x + 1 }$ from the graph of $y = \sqrt { x }$

Given $g ( x ) = \left\{ \begin{array} { c c } 3 & x < 1 \\\sqrt { x + 1 } & x \geq 1\end{array} \right.$ Find $g \left( t ^ { 2 } - 1 \right)$

Limits

Derivatives

Applications of the Derivative

Definite Integrals

Techniques of Integration

Applications of Integration

Sequences and Series

Power Series

Parametric Equations Polar Coordinates and Conic Sections

Vectors

Vector Functions

Multivariable Functions

Double and Triple Integrals

Vector Analysis

Filters

Exam 15: Functions and Precalculus

Given f(x)=x2+x−2x−1f ( x ) = \frac { x ^ { 2 } + x - 2 } { x - 1 }f(x)=x−1x2+x−2​ , find a linear function ggg which is identical to fff

Find the domain and range of the piecewise defined function: f(x)={−1x≤−51x−5<x<5x−5x>5f ( x ) = \left\{ \begin{array} { c c } - 1 & x \leq - 5 \\\frac { 1 } { x } & - 5 < x < 5 \\x - 5 & x > 5\end{array} \right.f(x)=⎩⎨⎧​−1x1​x−5​x≤−5−5<x<5x>5​

(-3, 4) is on the graph of an odd function f(x)f ( x )f(x) find another point on the graph of f(x)f ( x )f(x)

Given y=x2−4x−8y = x ^ { 2 } - 4 x - 8y=x2−4x−8 , for what value(s) of XXX is y=−3y = - 3y=−3 ?

Find the domain of f(x)=x2−9x+3f ( x ) = \frac { x ^ { 2 } - 9 } { \sqrt { x + 3 } }f(x)=x+3​x2−9​

Find the equation of a linear function whose graph passes through the points (2, -1) and (-3, 2).

Table below defines two functions fff and ggg Create an additional row for the table for the function (f∘g)(x)( f \circ g ) ( x )(f∘g)(x) x 0 1 2 3 4 5 6 f(x) 0 1 3 2 3 0 2 g(x) 1 0 1 1 0 1 0

Write f(x)=∣4−x2∣f ( x ) = \left| 4 - x ^ { 2 } \right|f(x)=​4−x2​ as a piecewise function.

Find the domain and range of f(x)=9−x2x+3f ( x ) = \frac { \sqrt { 9 - x ^ { 2 } } } { x + 3 }f(x)=x+39−x2​​

Which of the following points lie on the graph of f(x)=3x+4f ( x ) = \sqrt { 3 x + 4 }f(x)=3x+4​ ?A (-3, 6) B (4, 4) C (0, 4)

Is f(x)=2x3x2+2f ( x ) = \frac { 2 x ^ { 3 } } { x ^ { 2 } + 2 }f(x)=x2+22x3​ an even function, an odd function or neither? Explain.

Solve the following equation for t, on the interval [0,π][ 0 , \pi ][0,π] : 2cos⁡2t=22 \cos 2 t = \sqrt { 2 }2cos2t=2​

Write the following expression as an algebraic expression that does not involve trigonometric or inverse trigonometric functions cos⁡(2cos⁡−15x)\cos \left( 2 \cos ^ { - 1 } 5 x \right)cos(2cos−15x)

Write all the transformations applied to obtain the graph of y=∣2x+4∣−3y = | 2 x + 4 | - 3y=∣2x+4∣−3 from the graph of y=∣x∣y = | x |y=∣x∣

Write the following expression as an algebraic expression that does not involve trigonometric or inverse trigonometric functions tan⁡2(sec⁡−1x)\tan ^ { 2 } \left( \sec ^ { - 1 } x \right)tan2(sec−1x)

Write f(x)=5+∣3x−2∣f ( x ) = 5 + | 3 x - 2 |f(x)=5+∣3x−2∣ as a piecewise function.

Find an equation for a polynomial function whose graph passes through the points (3, 0), (-1, 0) and (-3, 0).

For the polynomial f(x)=x3(3−x)2(1+x2)f ( x ) = x ^ { 3 } ( 3 - x ) ^ { 2 } \left( 1 + x ^ { 2 } \right)f(x)=x3(3−x)2(1+x2) , determine the leading coefficient and the degree.

Write all the transformations applied to obtain the graph of y=2−x+1y = 2 - \sqrt { x + 1 }y=2−x+1​ from the graph of y=xy = \sqrt { x }y=x​

Given g(x)={3x<1x+1x≥1g ( x ) = \left\{ \begin{array} { c c } 3 & x < 1 \\\sqrt { x + 1 } & x \geq 1\end{array} \right.g(x)={3x+1​​x<1x≥1​ Find g(t2−1)g \left( t ^ { 2 } - 1 \right)g(t2−1)

Limits

Derivatives

Applications of the Derivative

Definite Integrals

Techniques of Integration

Applications of Integration

Sequences and Series

Power Series

Parametric Equations Polar Coordinates and Conic Sections

Vectors

Vector Functions

Multivariable Functions

Double and Triple Integrals

Vector Analysis

Filters

Given $f ( x ) = \frac { x ^ { 2 } + x - 2 } { x - 1 }$ , find a linear function $g$ which is identical to $f$

Find the domain and range of the piecewise defined function: $f ( x ) = \left\{ \begin{array} { c c } - 1 & x \leq - 5 \\\frac { 1 } { x } & - 5 < x < 5 \\x - 5 & x > 5\end{array} \right.$

(-3, 4) is on the graph of an odd function $f ( x )$ find another point on the graph of $f ( x )$

Given $y = x ^ { 2 } - 4 x - 8$ , for what value(s) of $X$ is $y = - 3$ ?

Find the domain of $f ( x ) = \frac { x ^ { 2 } - 9 } { \sqrt { x + 3 } }$

Table below defines two functions $f$ and $g$ Create an additional row for the table for the function $( f \circ g ) ( x )$ x 0 1 2 3 4 5 6 f(x) 0 1 3 2 3 0 2 g(x) 1 0 1 1 0 1 0

Write $f ( x ) = \left| 4 - x ^ { 2 } \right|$ as a piecewise function.

Find the domain and range of $f ( x ) = \frac { \sqrt { 9 - x ^ { 2 } } } { x + 3 }$

Which of the following points lie on the graph of $f ( x ) = \sqrt { 3 x + 4 }$ ?A (-3, 6) B (4, 4) C (0, 4)

Is $f ( x ) = \frac { 2 x ^ { 3 } } { x ^ { 2 } + 2 }$ an even function, an odd function or neither? Explain.

Solve the following equation for t, on the interval $[ 0 , \pi ]$ : $2 \cos 2 t = \sqrt { 2 }$

Write the following expression as an algebraic expression that does not involve trigonometric or inverse trigonometric functions $\cos \left( 2 \cos ^ { - 1 } 5 x \right)$

Write all the transformations applied to obtain the graph of $y = | 2 x + 4 | - 3$ from the graph of $y = | x |$

Write the following expression as an algebraic expression that does not involve trigonometric or inverse trigonometric functions $\tan ^ { 2 } \left( \sec ^ { - 1 } x \right)$

Write $f ( x ) = 5 + | 3 x - 2 |$ as a piecewise function.

For the polynomial $f ( x ) = x ^ { 3 } ( 3 - x ) ^ { 2 } \left( 1 + x ^ { 2 } \right)$ , determine the leading coefficient and the degree.

Write all the transformations applied to obtain the graph of $y = 2 - \sqrt { x + 1 }$ from the graph of $y = \sqrt { x }$

Given $g ( x ) = \left\{ \begin{array} { c c } 3 & x < 1 \\\sqrt { x + 1 } & x \geq 1\end{array} \right.$ Find $g \left( t ^ { 2 } - 1 \right)$