Question 1

Find the domain of $f ( x ) = \frac { \ln ( x - 3 ) } { \ln ( x + 1 ) }$

Accepted Answer

A)  (-1, $\infty$ ) 
B)  $( - 1,0 ) \cup ( 0 , \infty )$ 
C)  (3, $\infty$ ) 
D)  [3, $\infty$ ) 
A)  (-1, $\infty$ ) 
B)  $( - 1,0 ) \cup ( 0 , \infty )$ 
C)  (3, $\infty$ ) 
D)  [3, $\infty$ )

Question 2

Suppose (3, 7) is a point on the graph of $f ( x )$ , find a point on the graph of $f ( x - 2 )$

Accepted Answer

A)  (-2, 7) 
B)  (3, 5) 
C)  (1, 7) 
D)  (1,5) 
A)  (-2, 7) 
B)  (3, 5) 
C)  (1, 7) 
D)  (1,5)

Question 3

Write all the transformations applied to obtain the graph of $y = - x ^ { 2 } + 4 x$ from the graph of $y = x ^ { 2 }$

Accepted Answer

Graph of @#LAT-DLM& is shifted right 2 u

Question 4

Solve the following equation for x $\cos \left( \sin ^ { - 1 } x \right) = 0$

Accepted Answer

The answer of Solve the following equation for x \(\cos...

Question 5

Find the average rate of change of the function $f ( x ) = \sqrt { x + 1 }$ on the interval [0, 8].

Accepted Answer

A)  8/3 
B)  3/8 
C)  1/4 
D)  -1/4 
A)  8/3 
B)  3/8 
C)  1/4 
D)  -1/4

Question 6

Is $g ( x ) = \frac { - 3 } { x ^ { 2 } + 1 }$ an even function, an odd function or neither? Explain.

Accepted Answer

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

Question 7

Explain why the graph of $f ( x ) = \frac { ( x - 2 ) ( x + 3 ) } { ( x + 3 ) ^ { 2 } }$ does not have a hole in it at $x = - 3$ ?

Accepted Answer

Because it

Question 8

Solve the following equation for $X$ : $e ^ { x } - 4 x e ^ { x } = 0$

Accepted Answer

A)  0 
B)  0 and $1 / 4$ 
C)  $1 / 4$ 
D)  4 
A)  0 
B)  0 and $1 / 4$ 
C)  $1 / 4$ 
D)  4

Question 9

Find an equation for a power function whose graph passes through the points (0, 0) and (2, 5).

Accepted Answer

@#LAT-DLM& Note that

Question 10

Is $f ( x ) = \sin ^ { 2 } x$ an even function, odd function or neither?

Accepted Answer

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

Question 11

(2, 3) is on the graph of an even function $g ( x )$ find another point on the graph of $g ( x )$

Accepted Answer

A)  (2, -3) 
B)  (-2, -3) 
C)  (-2, 3) 
D)  (-3, 2) 
A)  (2, -3) 
B)  (-2, -3) 
C)  (-2, 3) 
D)  (-3, 2)

Question 12

Find the inverse of $f ( x ) = - \sqrt { 2 - 5 x }$

Accepted Answer

The answer of Find the inverse of \(f ( x...

Question 13

Express $f ( x ) = \left( 2 + \cos \left( x ^ { 3 } \right) \right) ^ { 2 }$ as a composition of two functions: $g$ and $h$ such that $f = g \circ h$

Accepted Answer

The answer of Express \(f ( x ) = \left(...

Question 14

Complete the entries in the table below to make $f$ an even function
 $$\begin{array} { | l | l | l | l | l | l | l | l | } 
\hline x & - 3 & - 2 & - 1 & 0 & 1 & 2 & 3 \
\hline f ( x ) & 5 & & - 2 & & & 3 & \
\hline
\end{array}$$

Accepted Answer

The answer of Complete the entries in the table below...

Question 15

Solve the following equation for $X$ : $\ln ( 6 x ) - 3 \ln \left( x ^ { 2 } \right) = \ln ( 3 )$

Accepted Answer

A)  $2 ^ { 5 }$ 
B)  2 
C)  ln(2) 
D)  $\sqrt [ 5 ] { 2 }$ 
A)  $2 ^ { 5 }$ 
B)  2 
C)  ln(2) 
D)  $\sqrt [ 5 ] { 2 }$

Question 16

Expand the logarithm in terms of sums and differences: $$\ln \frac { x ^ { 3 } \cos ^ { 2 } x } { \sqrt { x ^ { 2 } + 1 } }$$

Accepted Answer

The answer of Expand the logarithm in terms of sums...

Question 17

Suppose (3, 7) is a point on the graph of $f ( x )$ , find a point on the graph of $2 f ( x + 1 ) - 3$

Accepted Answer

A)  (4, 7) 
B)  (4, 14) 
C)  (4, 11) 
D)  (8, 11) 
A)  (4, 7) 
B)  (4, 14) 
C)  (4, 11) 
D)  (8, 11)

Question 18

Find the equation of a linear function whose graph is perpendicular to $x - 2 y + 2 = 0$ and passes through the point (1, 3).

Accepted Answer

A)  $y = - 2 x - 5$ 
B)  $y = - 2 x + 1$ 
C)  $y = - 2 x + 5$ 
D)  $y = 2 x - 5$ 
A)  $y = - 2 x - 5$ 
B)  $y = - 2 x + 1$ 
C)  $y = - 2 x + 5$ 
D)  $y = 2 x - 5$

Question 19

Let $f ( x ) = 2 x ^ { 3 } + 3 x + 1$ Find $X$ if $f ^ { - 1 } ( x ) = - 1$

Accepted Answer

A)  3/2 
B)  -4 
C)  0 
D)  4 
A)  3/2 
B)  -4 
C)  0 
D)  4

Question 20

Sketch the graph of a possible rational function $f$ with roots at $x = - 1$ and $x = 3$ , a vertical asymptote at $x = 2$ , and a horizontal asymptote at $y = - 2$

Accepted Answer

One of the

Find the domain of $f ( x ) = \frac { \ln ( x - 3 ) } { \ln ( x + 1 ) }$

Suppose (3, 7) is a point on the graph of $f ( x )$ , find a point on the graph of $f ( x - 2 )$

Write all the transformations applied to obtain the graph of $y = - x ^ { 2 } + 4 x$ from the graph of $y = x ^ { 2 }$

Solve the following equation for x $\cos \left( \sin ^ { - 1 } x \right) = 0$

Find the average rate of change of the function $f ( x ) = \sqrt { x + 1 }$ on the interval [0, 8].

Is $g ( x ) = \frac { - 3 } { x ^ { 2 } + 1 }$ an even function, an odd function or neither? Explain.

Explain why the graph of $f ( x ) = \frac { ( x - 2 ) ( x + 3 ) } { ( x + 3 ) ^ { 2 } }$ does not have a hole in it at $x = - 3$ ?

Solve the following equation for $X$ : $e ^ { x } - 4 x e ^ { x } = 0$

Find an equation for a power function whose graph passes through the points (0, 0) and (2, 5).

Is $f ( x ) = \sin ^ { 2 } x$ an even function, odd function or neither?

(2, 3) is on the graph of an even function $g ( x )$ find another point on the graph of $g ( x )$

Find the inverse of $f ( x ) = - \sqrt { 2 - 5 x }$

Express $f ( x ) = \left( 2 + \cos \left( x ^ { 3 } \right) \right) ^ { 2 }$ as a composition of two functions: $g$ and $h$ such that $f = g \circ h$

Complete the entries in the table below to make $f$ an even function x -3 -2 -1 0 1 2 3 f(x) 5 -2 3

Solve the following equation for $X$ : $\ln ( 6 x ) - 3 \ln \left( x ^ { 2 } \right) = \ln ( 3 )$

Expand the logarithm in terms of sums and differences: $\ln \frac { x ^ { 3 } \cos ^ { 2 } x } { \sqrt { x ^ { 2 } + 1 } }$

Suppose (3, 7) is a point on the graph of $f ( x )$ , find a point on the graph of $2 f ( x + 1 ) - 3$

Find the equation of a linear function whose graph is perpendicular to $x - 2 y + 2 = 0$ and passes through the point (1, 3).

Let $f ( x ) = 2 x ^ { 3 } + 3 x + 1$ Find $X$ if $f ^ { - 1 } ( x ) = - 1$

Sketch the graph of a possible rational function $f$ with roots at $x = - 1$ and $x = 3$ , a vertical asymptote at $x = 2$ , and a horizontal asymptote at $y = - 2$

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

Find the domain of f(x)=ln⁡(x−3)ln⁡(x+1)f ( x ) = \frac { \ln ( x - 3 ) } { \ln ( x + 1 ) }f(x)=ln(x+1)ln(x−3)​

Suppose (3, 7) is a point on the graph of f(x)f ( x )f(x) , find a point on the graph of f(x−2)f ( x - 2 )f(x−2)

Write all the transformations applied to obtain the graph of y=−x2+4xy = - x ^ { 2 } + 4 xy=−x2+4x from the graph of y=x2y = x ^ { 2 }y=x2

Solve the following equation for x cos⁡(sin⁡−1x)=0\cos \left( \sin ^ { - 1 } x \right) = 0cos(sin−1x)=0

Find the average rate of change of the function f(x)=x+1f ( x ) = \sqrt { x + 1 }f(x)=x+1​ on the interval [0, 8].

Is g(x)=−3x2+1g ( x ) = \frac { - 3 } { x ^ { 2 } + 1 }g(x)=x2+1−3​ an even function, an odd function or neither? Explain.

Explain why the graph of f(x)=(x−2)(x+3)(x+3)2f ( x ) = \frac { ( x - 2 ) ( x + 3 ) } { ( x + 3 ) ^ { 2 } }f(x)=(x+3)2(x−2)(x+3)​ does not have a hole in it at x=−3x = - 3x=−3 ?

Solve the following equation for XXX : ex−4xex=0e ^ { x } - 4 x e ^ { x } = 0ex−4xex=0

Find an equation for a power function whose graph passes through the points (0, 0) and (2, 5).

Is f(x)=sin⁡2xf ( x ) = \sin ^ { 2 } xf(x)=sin2x an even function, odd function or neither?

(2, 3) is on the graph of an even function g(x)g ( x )g(x) find another point on the graph of g(x)g ( x )g(x)

Find the inverse of f(x)=−2−5xf ( x ) = - \sqrt { 2 - 5 x }f(x)=−2−5x​

Express f(x)=(2+cos⁡(x3))2f ( x ) = \left( 2 + \cos \left( x ^ { 3 } \right) \right) ^ { 2 }f(x)=(2+cos(x3))2 as a composition of two functions: ggg and hhh such that f=g∘hf = g \circ hf=g∘h

Complete the entries in the table below to make fff an even function x -3 -2 -1 0 1 2 3 f(x) 5 -2 3

Solve the following equation for XXX : ln⁡(6x)−3ln⁡(x2)=ln⁡(3)\ln ( 6 x ) - 3 \ln \left( x ^ { 2 } \right) = \ln ( 3 )ln(6x)−3ln(x2)=ln(3)

Expand the logarithm in terms of sums and differences: ln⁡x3cos⁡2xx2+1\ln \frac { x ^ { 3 } \cos ^ { 2 } x } { \sqrt { x ^ { 2 } + 1 } }lnx2+1​x3cos2x​

Suppose (3, 7) is a point on the graph of f(x)f ( x )f(x) , find a point on the graph of 2f(x+1)−32 f ( x + 1 ) - 32f(x+1)−3

Find the equation of a linear function whose graph is perpendicular to x−2y+2=0x - 2 y + 2 = 0x−2y+2=0 and passes through the point (1, 3).

Let f(x)=2x3+3x+1f ( x ) = 2 x ^ { 3 } + 3 x + 1f(x)=2x3+3x+1 Find XXX if f−1(x)=−1f ^ { - 1 } ( x ) = - 1f−1(x)=−1

Sketch the graph of a possible rational function fff with roots at x=−1x = - 1x=−1 and x=3x = 3x=3 , a vertical asymptote at x=2x = 2x=2 , and a horizontal asymptote at y=−2y = - 2y=−2

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

Find the domain of $f ( x ) = \frac { \ln ( x - 3 ) } { \ln ( x + 1 ) }$

Suppose (3, 7) is a point on the graph of $f ( x )$ , find a point on the graph of $f ( x - 2 )$

Write all the transformations applied to obtain the graph of $y = - x ^ { 2 } + 4 x$ from the graph of $y = x ^ { 2 }$

Solve the following equation for x $\cos \left( \sin ^ { - 1 } x \right) = 0$

Find the average rate of change of the function $f ( x ) = \sqrt { x + 1 }$ on the interval [0, 8].

Is $g ( x ) = \frac { - 3 } { x ^ { 2 } + 1 }$ an even function, an odd function or neither? Explain.

Explain why the graph of $f ( x ) = \frac { ( x - 2 ) ( x + 3 ) } { ( x + 3 ) ^ { 2 } }$ does not have a hole in it at $x = - 3$ ?

Solve the following equation for $X$ : $e ^ { x } - 4 x e ^ { x } = 0$

Is $f ( x ) = \sin ^ { 2 } x$ an even function, odd function or neither?

(2, 3) is on the graph of an even function $g ( x )$ find another point on the graph of $g ( x )$

Find the inverse of $f ( x ) = - \sqrt { 2 - 5 x }$

Express $f ( x ) = \left( 2 + \cos \left( x ^ { 3 } \right) \right) ^ { 2 }$ as a composition of two functions: $g$ and $h$ such that $f = g \circ h$

Complete the entries in the table below to make $f$ an even function x -3 -2 -1 0 1 2 3 f(x) 5 -2 3

Solve the following equation for $X$ : $\ln ( 6 x ) - 3 \ln \left( x ^ { 2 } \right) = \ln ( 3 )$

Expand the logarithm in terms of sums and differences: $\ln \frac { x ^ { 3 } \cos ^ { 2 } x } { \sqrt { x ^ { 2 } + 1 } }$

Suppose (3, 7) is a point on the graph of $f ( x )$ , find a point on the graph of $2 f ( x + 1 ) - 3$

Find the equation of a linear function whose graph is perpendicular to $x - 2 y + 2 = 0$ and passes through the point (1, 3).

Let $f ( x ) = 2 x ^ { 3 } + 3 x + 1$ Find $X$ if $f ^ { - 1 } ( x ) = - 1$

Sketch the graph of a possible rational function $f$ with roots at $x = - 1$ and $x = 3$ , a vertical asymptote at $x = 2$ , and a horizontal asymptote at $y = - 2$