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, $\infty$ )

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)

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

The answer of Write all the transformations applied to obtain...

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

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

The answer of Explain why the graph of \(f (...

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

Question 9

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

Accepted Answer

The answer of Find an equation for a power function...

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)

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)  $\sqrt [ 5 ] { 2 }$

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)

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)  $y = 2 x - 5$

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

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

The answer of Sketch the graph of a possible rational...

Exam 15: Functions and Precalculus

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 $\begin{array} { | l | l | l | l | l | l | l | l | } \hline x & - 3 & - 2 & - 1 & 0 & 1 & 2 & 3 \\\hline f ( x ) & 5 & & - 2 & & & 3 & \\\hline\end{array}$

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 $y = - 2$

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

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

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 $f = g \circ h$

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 $y = - 2$