Question 1

The graph of f is given. Sketch the graph of $f^{-1}$ on the same set of axes.   3

Accepted Answer

The answer of The graph of f is given. Sketch...

Question 2

Find the domain of the function. $f(x)=\frac{6}{1-e^{x}}$

Accepted Answer

The answer of Find the domain of the function. $f(x)=\frac{6}{1-e^{x}}$...

Question 3

Find the exact value of the given expression. sin $\left(\sin ^{-1}\left(-\frac{\sqrt{3}}{2}\right)\right)$

Accepted Answer

A)  $-\frac{\sqrt{3}}{2}$ 
B)  $-\frac{1}{2}$ 
C)  1 
D)  0 
A)  $-\frac{\sqrt{3}}{2}$ 
B)  $-\frac{1}{2}$ 
C)  1 
D)  0

Question 4

Express the function in the form of $f \circ g \circ h$ . $H(x)=2-4^{x^{3}}$

Accepted Answer

The answer of Express the function in the form of...

Question 5

Graph the function by hand, not by plotting points, but by starting with the graph of one of the standard functions and then applying the appropriate transformations. $y=4+2 x-x^{2}$

Accepted Answer

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

Question 6

Find the exact value of the given expression. cos-1 0

Accepted Answer

A)  $\pi$ 
B)  $\frac{\pi}{2}$ 
C)  2 $\pi$ 
D)  $\frac{2}{\pi}$ 
A)  $\pi$ 
B)  $\frac{\pi}{2}$ 
C)  2 $\pi$ 
D)  $\frac{2}{\pi}$

Question 7

If the point $(7,3)$ is on the graph of an even function, what other point must also be on the graph?

Accepted Answer

A)  $(-7,-3)$ 
B)  $(7,-3)$ 
C)  $(0,0)$ 
D)  $(-7,3)$ 
E)  None of these 
A)  $(-7,-3)$ 
B)  $(7,-3)$ 
C)  $(0,0)$ 
D)  $(-7,3)$ 
E)  None of these

Question 8

Use the Law of Exponents to rewrite and simplify the expression. $\frac{\sqrt{a \sqrt{b}}}{\sqrt[7]{a b}}$

Accepted Answer

A)  $a^{\frac{5}{14}} b^{\frac{3}{28}}$ 
B)  $\frac{a}{b^{\frac{3}{28}}}$ 
C)  $\frac{a}{b}$ 
D)  $\frac{a^{\frac{5}{14}}}{b^{\frac{3}{28}}}$ 
E)  $\left(\frac{a}{b}\right)^{\frac{5}{14}}$ 
A)  $a^{\frac{5}{14}} b^{\frac{3}{28}}$ 
B)  $\frac{a}{b^{\frac{3}{28}}}$ 
C)  $\frac{a}{b}$ 
D)  $\frac{a^{\frac{5}{14}}}{b^{\frac{3}{28}}}$ 
E)  $\left(\frac{a}{b}\right)^{\frac{5}{14}}$

Question 9

If f (x) = $\left\{\begin{array}{cc}
x^{2}+3 & \text { if } x \leq 0 \
\sqrt{x} & \text { if } x>0
\end{array}\right.$ find f (-4), f (0), and f (1).

Accepted Answer

The answer of If f (x) = \(\left\{\begin{array}{cc}
x^{2}+3 & \text...

Question 10

In the function $f(x)=2 x+d$ , what must be the value d, if $f(3)=1$ ?

Accepted Answer

A)  $d=7$ 
B)  $d=5$ 
C)  $d=-5$ 
D)  $d=-1$ 
E)  $d=-7$ 
A)  $d=7$ 
B)  $d=5$ 
C)  $d=-5$ 
D)  $d=-1$ 
E)  $d=-7$

Question 11

Find the domain of the function $f(x)=\frac{x}{-2 \sin x-3}$

Accepted Answer

A)  $[2,3]$ 
B)  $[-3,-2]$ 
C)  $\left[-\frac{3}{2}, \infty\right)$ 
D)  $(-\infty, \infty)$ 
A)  $[2,3]$ 
B)  $[-3,-2]$ 
C)  $\left[-\frac{3}{2}, \infty\right)$ 
D)  $(-\infty, \infty)$

Question 12

The graph shown gives the weight of a certain person as a function of age. Find the age at which the person started an exercise program.

Accepted Answer

A)  20 
B)  54 
C)  38 
D)  30 
E)  35 
A)  20 
B)  54 
C)  38 
D)  30 
E)  35

Question 13

Plot the graph of the function f in an appropriate viewing window. $f(x)=x+0.03 \sin 50 x$

Accepted Answer

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

Question 14

If $f(x)=x+5$ and $h(x)=4 x-10$ , find a function g such that $g \circ f=h$ .

Accepted Answer

A)  $g(x)=4 x+30$ 
B)  $g(x)=4 x$ 
C)  $g(x)=x-30$ 
D)    
E)  $g(x)=x+30$ 
A)  $g(x)=4 x+30$ 
B)  $g(x)=4 x$ 
C)  $g(x)=x-30$ 
D)    
E)  $g(x)=x+30$

Question 15

Find the domain, range, and x-intercept(s) of the function. $f(x)=\ln (x-2)-1$

Accepted Answer

Domain: @#LAT-DLM& R

Question 16

Find the points of intersection of the graphs of the functions. Express your answers accurate to five decimal places. $f(x)$ = 0.2 $x^{2}$ - 1.3x - 3.7; $g(x)$ = -0.1 $x^{2}$ + 0.2x + 6.4

Accepted Answer

(–3.81796,

Question 17

Which of the following graphs is the graph of the function? $f(x)=\sin |2 x|$

Accepted Answer

A)  Graph 2 
B)  Graph 1 
C)  Graph 3 
A)  Graph 2 
B)  Graph 1 
C)  Graph 3

Question 18

Find $f^{-1}$ (a) for the function f and the real number a. $f(x)=x^{3}+x-2$ ; $a=-2$

Accepted Answer

A)  2 
B)  -1 
C)  1 
D)  0 
A)  2 
B)  -1 
C)  1 
D)  0

Question 19

If $f(x)=3 x+\ln x$ , find $f^{-1}(7)$ .

Accepted Answer

The answer of If $f(x)=3 x+\ln x$ , find $f^{-1}(7)$...

Question 20

A rectangle has perimeter 14 m. Express the area of the rectangle as a function $A(l)$ of the length $l$ of one of its sides.

Accepted Answer

A)  $A(l)=7 l-l^{2}$ 
B)  $A(l)=l-7 l^{2}$ 
C)  $A(l)=14 l-l^{2}$ 
D)  $A(l)=14 l+l^{2}$ 
E)  $A(l)=7 l+l^{2}$ 
A)  $A(l)=7 l-l^{2}$ 
B)  $A(l)=l-7 l^{2}$ 
C)  $A(l)=14 l-l^{2}$ 
D)  $A(l)=14 l+l^{2}$ 
E)  $A(l)=7 l+l^{2}$

The graph of f is given. Sketch the graph of $f^{-1}$ on the same set of axes. $The graph of f is given. Sketch the graph of f^{-1} on the same set of axes. 3$ 3

Find the domain of the function. $f(x)=\frac{6}{1-e^{x}}$

Find the exact value of the given expression. sin $\left(\sin ^{-1}\left(-\frac{\sqrt{3}}{2}\right)\right)$

Express the function in the form of $f \circ g \circ h$ . $H(x)=2-4^{x^{3}}$

Graph the function by hand, not by plotting points, but by starting with the graph of one of the standard functions and then applying the appropriate transformations. $y=4+2 x-x^{2}$

Find the exact value of the given expression. cos^-¹ 0

If the point $(7,3)$ is on the graph of an even function, what other point must also be on the graph?

Use the Law of Exponents to rewrite and simplify the expression. $\frac{\sqrt{a \sqrt{b}}}{\sqrt[7]{a b}}$

If f (x) = $\left\{\begin{array}{cc}x^{2}+3 & \text { if } x \leq 0 \\\sqrt{x} & \text { if } x>0\end{array}\right.$ find f (-4), f (0), and f (1).

In the function $f(x)=2 x+d$ , what must be the value d, if $f(3)=1$ ?

Find the domain of the function $f(x)=\frac{x}{-2 \sin x-3}$

The graph shown gives the weight of a certain person as a function of age. Find the age at which the person started an exercise program.

Plot the graph of the function f in an appropriate viewing window. $f(x)=x+0.03 \sin 50 x$

If $f(x)=x+5$ and $h(x)=4 x-10$ , find a function g such that $g \circ f=h$ .

Find the domain, range, and x-intercept(s) of the function. $f(x)=\ln (x-2)-1$

Find the points of intersection of the graphs of the functions. Express your answers accurate to five decimal places. $f(x)$ = 0.2 $x^{2}$ - 1.3x - 3.7; $g(x)$ = -0.1 $x^{2}$ + 0.2x + 6.4

Find $f^{-1}$ (a) for the function f and the real number a. $f(x)=x^{3}+x-2$ ; $a=-2$

If $f(x)=3 x+\ln x$ , find $f^{-1}(7)$ .

A rectangle has perimeter 14 m. Express the area of the rectangle as a function $A(l)$ of the length $l$ of one of its sides.

Derivatives

Applications of Differentiation

Integrals

Applications of Integration

Inverse Functions

Techniques of Integration

Further Applications of Integration

Differential Equations

Parametric Equations and Polar Coordinates

Infinite Sequences and Series

Vectors and the Geometry of Space

Vector Functions

Partial Derivatives

Multiple Integrals

Vector Calculus

Second-Order Differential Equations

Final Exam

Filters

Exam 1: Functions and Limits

The graph of f is given. Sketch the graph of f−1f^{-1}f−1 on the same set of axes. 3

Find the domain of the function. f(x)=61−exf(x)=\frac{6}{1-e^{x}}f(x)=1−ex6​

Find the exact value of the given expression. sin (sin⁡−1(−32))\left(\sin ^{-1}\left(-\frac{\sqrt{3}}{2}\right)\right)(sin−1(−23​​))

Express the function in the form of f∘g∘hf \circ g \circ hf∘g∘h . H(x)=2−4x3H(x)=2-4^{x^{3}}H(x)=2−4x3

Graph the function by hand, not by plotting points, but by starting with the graph of one of the standard functions and then applying the appropriate transformations. y=4+2x−x2y=4+2 x-x^{2}y=4+2x−x2

Find the exact value of the given expression. cos-1 0

If the point (7,3)(7,3)(7,3) is on the graph of an even function, what other point must also be on the graph?

Use the Law of Exponents to rewrite and simplify the expression. abab7\frac{\sqrt{a \sqrt{b}}}{\sqrt[7]{a b}}7ab​ab​​​

If f (x) = {x2+3 if x≤0x if x>0\left\{\begin{array}{cc}x^{2}+3 & \text { if } x \leq 0 \\\sqrt{x} & \text { if } x>0\end{array}\right.{x2+3x​​ if x≤0 if x>0​ find f (-4), f (0), and f (1).

In the function f(x)=2x+df(x)=2 x+df(x)=2x+d , what must be the value d, if f(3)=1f(3)=1f(3)=1 ?

Find the domain of the function f(x)=x−2sin⁡x−3f(x)=\frac{x}{-2 \sin x-3}f(x)=−2sinx−3x​

The graph shown gives the weight of a certain person as a function of age. Find the age at which the person started an exercise program.

Plot the graph of the function f in an appropriate viewing window. f(x)=x+0.03sin⁡50xf(x)=x+0.03 \sin 50 xf(x)=x+0.03sin50x

If f(x)=x+5f(x)=x+5f(x)=x+5 and h(x)=4x−10h(x)=4 x-10h(x)=4x−10 , find a function g such that g∘f=hg \circ f=hg∘f=h .

Find the domain, range, and x-intercept(s) of the function. f(x)=ln⁡(x−2)−1f(x)=\ln (x-2)-1f(x)=ln(x−2)−1

Find the points of intersection of the graphs of the functions. Express your answers accurate to five decimal places. f(x)f(x)f(x) = 0.2 x2x^{2}x2 - 1.3x - 3.7; g(x)g(x)g(x) = -0.1 x2x^{2}x2 + 0.2x + 6.4

Which of the following graphs is the graph of the function? f(x)=sin⁡∣2x∣f(x)=\sin |2 x|f(x)=sin∣2x∣

Find f−1f^{-1}f−1 (a) for the function f and the real number a. f(x)=x3+x−2f(x)=x^{3}+x-2f(x)=x3+x−2 ; a=−2a=-2a=−2

If f(x)=3x+ln⁡xf(x)=3 x+\ln xf(x)=3x+lnx , find f−1(7)f^{-1}(7)f−1(7) .

A rectangle has perimeter 14 m. Express the area of the rectangle as a function A(l)A(l)A(l) of the length lll of one of its sides.

Derivatives

Applications of Differentiation

Integrals

Applications of Integration

Inverse Functions

Techniques of Integration

Further Applications of Integration

Differential Equations

Parametric Equations and Polar Coordinates

Infinite Sequences and Series

Vectors and the Geometry of Space

Vector Functions

Partial Derivatives

Multiple Integrals

Vector Calculus

Second-Order Differential Equations

Final Exam

Filters

The graph of f is given. Sketch the graph of $f^{-1}$ on the same set of axes. $The graph of f is given. Sketch the graph of f^{-1} on the same set of axes. 3$ 3

Find the domain of the function. $f(x)=\frac{6}{1-e^{x}}$

Find the exact value of the given expression. sin $\left(\sin ^{-1}\left(-\frac{\sqrt{3}}{2}\right)\right)$

Express the function in the form of $f \circ g \circ h$ . $H(x)=2-4^{x^{3}}$

Graph the function by hand, not by plotting points, but by starting with the graph of one of the standard functions and then applying the appropriate transformations. $y=4+2 x-x^{2}$

Find the exact value of the given expression. cos^-¹ 0

If the point $(7,3)$ is on the graph of an even function, what other point must also be on the graph?

Use the Law of Exponents to rewrite and simplify the expression. $\frac{\sqrt{a \sqrt{b}}}{\sqrt[7]{a b}}$

If f (x) = $\left\{\begin{array}{cc}x^{2}+3 & \text { if } x \leq 0 \\\sqrt{x} & \text { if } x>0\end{array}\right.$ find f (-4), f (0), and f (1).

In the function $f(x)=2 x+d$ , what must be the value d, if $f(3)=1$ ?

Find the domain of the function $f(x)=\frac{x}{-2 \sin x-3}$

Plot the graph of the function f in an appropriate viewing window. $f(x)=x+0.03 \sin 50 x$

If $f(x)=x+5$ and $h(x)=4 x-10$ , find a function g such that $g \circ f=h$ .

Find the domain, range, and x-intercept(s) of the function. $f(x)=\ln (x-2)-1$

Find the points of intersection of the graphs of the functions. Express your answers accurate to five decimal places. $f(x)$ = 0.2 $x^{2}$ - 1.3x - 3.7; $g(x)$ = -0.1 $x^{2}$ + 0.2x + 6.4

Find $f^{-1}$ (a) for the function f and the real number a. $f(x)=x^{3}+x-2$ ; $a=-2$

If $f(x)=3 x+\ln x$ , find $f^{-1}(7)$ .

A rectangle has perimeter 14 m. Express the area of the rectangle as a function $A(l)$ of the length $l$ of one of its sides.