Question 1

Find the exponential function $f(x)=C a^{x}$ whose graph is given.

Accepted Answer

A)  $f(x)=2\left(\frac{1}{3}\right)^{x}$ 
B)  $f(x)=3\left(\frac{1}{3}\right)^{x}$ 
C)  $f(x)=\left(\frac{3}{2}\right)^{x}$ 
D)  $f(x)=\frac{1}{3^{x}}$ 
E)  $f(x)=\left(\frac{3}{4}\right)^{x}$ 
A)  $f(x)=2\left(\frac{1}{3}\right)^{x}$ 
B)  $f(x)=3\left(\frac{1}{3}\right)^{x}$ 
C)  $f(x)=\left(\frac{3}{2}\right)^{x}$ 
D)  $f(x)=\frac{1}{3^{x}}$ 
E)  $f(x)=\left(\frac{3}{4}\right)^{x}$ A

Question 2

If $f(x)=x^{2}-x+6$ , evaluate the difference quotient $\frac{f(a+h)-f(a)}{h}$ .

Accepted Answer

A)  $2 a-h-6$ 
B)  $2 a-6$ 
C)  h 
D)  $2 a+h-6$ 
E)  none of these 
A)  $2 a-h-6$ 
B)  $2 a-6$ 
C)  h 
D)  $2 a+h-6$ 
E)  none of these E

Question 3

Plot the graph of the function f in an appropriate viewing window.
f (x) = 5x 3 - 3x 2 + 2x   + 33

Accepted Answer

The answer of Plot the graph of the function f...

Question 4

The function $f(x)=\sqrt{5+c x^{2}}$ is graphed below.

Accepted Answer

A) $c=0$ B) $c>0$ C) $c<0$ A) $c=0$ B) $c>0$ C) $c<0$

Question 5

Sandy wishes to have a rectangular garden in her backyard. She has 40 ft of fencing with which to enclose her garden. Letting x denote the width of the garden, find a function f in the variable x that gives the area of the garden.

Accepted Answer

A)  $f(x)=40 x-x^{2}, \quad 0 $ $< x$   $<20$. 
B)  $f(x)=20 x-x^{2}, \quad 0 $ $< x$   $<20$ 
C)  $f(x)=40 x-x^{2}, \quad 0 $ $< x$   $<40$ 
D)  $f(x)=20 x-x^{2}, \quad 0 $ $< x$   $<20$. 
A)  $f(x)=40 x-x^{2}, \quad 0 $ $< x$   $<20$. 
B)  $f(x)=20 x-x^{2}, \quad 0 $ $< x$   $<20$ 
C)  $f(x)=40 x-x^{2}, \quad 0 $ $< x$   $<40$ 
D)  $f(x)=20 x-x^{2}, \quad 0 $ $< x$   $<20$.

Question 6

The relationship between the Fahrenheit and Celsius temperature scales is given by the linear function. $F=\frac{9}{5} C+32$ Complete the table and find the slope. $\begin{array}{|c|c|}
\hline{ }^{0} \mathrm{C} & { }^{0} \mathrm{~F} \
\hline 12 & \
\hline-19 & \
\hline \text { slope } & \
\hline
\end{array}$

Accepted Answer

The answer of The relationship between the Fahrenheit and Celsius...

Question 7

Find $f \circ g \circ h$ if $f(x)=\frac{1}{x}, \quad g(x)=2 x^{2}+7, \quad \text { and } \quad h(x)=\cos x$

Accepted Answer

The answer of Find $f \circ g \circ h$ if...

Question 8

Solve each equation for x.
(a) $\ln x=6$ (b) $e^{e^{x}}=5$

Accepted Answer

The answer of Solve each equation for x.
(a) $\ln x=6$...

Question 9

Many physical quantities are connected by inverse square laws, that is, by power functions of the form $f(x)=k x^{-2}$ . In particular, the illumination of an object by a light source is inversely proportional to the square of the distance from the source. Suppose that after dark you are in a room with just one lamp and you are trying to read a book. The light is too dim and so you move $\frac{1}{3} \text { th }$ the distance to the lamp. How much brighter is the light?

Accepted Answer

A)  $\frac{4}{9}$ times 
B)  $\frac{9}{2}$ times 
C)  9 times. 
D)  $\frac{3}{2}$ times 
E)  9 times 
A)  $\frac{4}{9}$ times 
B)  $\frac{9}{2}$ times 
C)  9 times. 
D)  $\frac{3}{2}$ times 
E)  9 times

Question 10

Use the Law of Exponents to rewrite and simplify the expression. $\frac{x^{4 x} \cdot x^{5 x+1}}{x^{x-5}}$

Accepted Answer

A)  $x^{8 x+6}$ 
B)  $x^{8 x+7}$ 
C)  $x^{6 x-10}$ 
D)  $x^{3 x+9}$ 
E)  $x^{4 \pi-8}$ 
A)  $x^{8 x+6}$ 
B)  $x^{8 x+7}$ 
C)  $x^{6 x-10}$ 
D)  $x^{3 x+9}$ 
E)  $x^{4 \pi-8}$

Question 11

Find the range of the function. $y=5+\cos x$

Accepted Answer

A)  $[4,6]$ 
B)  $(-1,3)$ 
C)  $(2, \infty)$ 
D)  $(-\infty, \infty)$ 
E)  $[-1,1]$ 
A)  $[4,6]$ 
B)  $(-1,3)$ 
C)  $(2, \infty)$ 
D)  $(-\infty, \infty)$ 
E)  $[-1,1]$

Question 12

Find all solutions of the equation correct to two decimal places. $x^{3}-9 x^{2}-40=0$

Accepted Answer

A)  $x=4.00$ , $x=9.05$ 
B)  $x=9.44$ 
C)  $x=-4.00$ , $x=9.05$ 
D)  $x=0$ , $x=4.01$ , $x=9.05$ 
E)  $x=0$ , $x=9.05$ 
A)  $x=4.00$ , $x=9.05$ 
B)  $x=9.44$ 
C)  $x=-4.00$ , $x=9.05$ 
D)  $x=0$ , $x=4.01$ , $x=9.05$ 
E)  $x=0$ , $x=9.05$

Question 13

The graphs of $f(x)$ and $g(x)$ are given. For what values of x is $f(x)=g(x)$ ?

Accepted Answer

A)  4, 2 
B)  0 
C)  -1 
D)  $-2,5$ 
E)  -4, 12 
A)  4, 2 
B)  0 
C)  -1 
D)  $-2,5$ 
E)  -4, 12

Question 14

Express the function in the form of $f \circ g$ . $v(t)=\sec \left(t^{4}\right) \tan \left(t^{4}\right)$ __________

Accepted Answer

None

Question 15

If $f(x)=4 x^{2}+2$ , find and simplify $\frac{f(1+h)-f(1)}{h}$ , where $h \neq 0$ .

Accepted Answer

A)  $2+4 h^{2}$ 
B)  $4+8 h$ 
C)  $4 h$ 
D)  $8+4 h$ 
A)  $2+4 h^{2}$ 
B)  $4+8 h$ 
C)  $4 h$ 
D)  $8+4 h$

Question 16

Find the solutions of the equation $\csc (2 \theta)=1$ in $[0,2 \pi)$ .

Accepted Answer

The answer of Find the solutions of the equation \(\csc...

Question 17

Simplify the expression. $e^{3 \ln 5}$

Accepted Answer

A)  8 
B)  15 
C)  125 
D)  243 
A)  8 
B)  15 
C)  125 
D)  243

Question 18

The monthly cost of driving a car depends on the number of miles driven. Julia found that in October it cost her $\$ 200$ to drive 300 mi and in July it cost her $\$ 350$ to drive 600 mi. Express the monthly cost C as a function of the distance driven d assuming that a linear relationship gives a suitable model.

Accepted Answer

A)  $C=-50 d+0.5$ 
B)  $C=-50 d-0.5$ 
C)  $C=0.5 d+50$ 
D)  $C=2 d+50$ 
E)  $C=0.5 d-50$ 
A)  $C=-50 d+0.5$ 
B)  $C=-50 d-0.5$ 
C)  $C=0.5 d+50$ 
D)  $C=2 d+50$ 
E)  $C=0.5 d-50$

Question 19

A stone is dropped into a lake, creating a circular ripple that travels outward at a speed of 45 cm/s. Express the radius r of this circle as a function of the time t (in seconds) and find $A \circ r$ if A is the area of this circle as a function of the radius.

Accepted Answer

The answer of A stone is dropped into a lake,...

Question 20

What is $\sqrt[10]{x}$ , given that $H=f \circ g \circ h$ and $H(x)=\sqrt[10]{\sqrt{x}-3}$ ?

Accepted Answer

A)  h(x) 
B)  g(x) 
C)  f(x) 
A)  h(x) 
B)  g(x) 
C)  f(x)

Find the exponential function $f(x)=C a^{x}$ whose graph is given. $Find the exponential function f(x)=C a^{x} whose graph is given.$

If $f(x)=x^{2}-x+6$ , evaluate the difference quotient $\frac{f(a+h)-f(a)}{h}$ .

Plot the graph of the function f in an appropriate viewing window. f (x) = 5x 3 - 3x 2 + 2x + 33

The function $f(x)=\sqrt{5+c x^{2}}$ is graphed below. $The function f(x)=\sqrt{5+c x^{2}} is graphed below.$

Sandy wishes to have a rectangular garden in her backyard. She has 40 ft of fencing with which to enclose her garden. Letting x denote the width of the garden, find a function f in the variable x that gives the area of the garden.

The relationship between the Fahrenheit and Celsius temperature scales is given by the linear function. $F=\frac{9}{5} C+32$ Complete the table and find the slope. 12 -19 slope

Find $f \circ g \circ h$ if $f(x)=\frac{1}{x}, \quad g(x)=2 x^{2}+7, \quad \text { and } \quad h(x)=\cos x$

Solve each equation for x. (a) $\ln x=6$ (b) $e^{e^{x}}=5$

Use the Law of Exponents to rewrite and simplify the expression. $\frac{x^{4 x} \cdot x^{5 x+1}}{x^{x-5}}$

Find the range of the function. $y=5+\cos x$

Find all solutions of the equation correct to two decimal places. $x^{3}-9 x^{2}-40=0$

The graphs of $f(x)$ and $g(x)$ are given. For what values of x is $f(x)=g(x)$ ?

Express the function in the form of $f \circ g$ . $v(t)=\sec \left(t^{4}\right) \tan \left(t^{4}\right)$ __________

If $f(x)=4 x^{2}+2$ , find and simplify $\frac{f(1+h)-f(1)}{h}$ , where $h \neq 0$ .

Find the solutions of the equation $\csc (2 \theta)=1$ in $[0,2 \pi)$ .

Simplify the expression. $e^{3 \ln 5}$

A stone is dropped into a lake, creating a circular ripple that travels outward at a speed of 45 cm/s. Express the radius r of this circle as a function of the time t (in seconds) and find $A \circ r$ if A is the area of this circle as a function of the radius.

What is $\sqrt[10]{x}$ , given that $H=f \circ g \circ h$ and $H(x)=\sqrt[10]{\sqrt{x}-3}$ ?

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

Find the exponential function f(x)=Caxf(x)=C a^{x}f(x)=Cax whose graph is given.

If f(x)=x2−x+6f(x)=x^{2}-x+6f(x)=x2−x+6 , evaluate the difference quotient f(a+h)−f(a)h\frac{f(a+h)-f(a)}{h}hf(a+h)−f(a)​ .

Plot the graph of the function f in an appropriate viewing window. f (x) = 5x 3 - 3x 2 + 2x + 33

The function f(x)=5+cx2f(x)=\sqrt{5+c x^{2}}f(x)=5+cx2​ is graphed below.

Sandy wishes to have a rectangular garden in her backyard. She has 40 ft of fencing with which to enclose her garden. Letting x denote the width of the garden, find a function f in the variable x that gives the area of the garden.

The relationship between the Fahrenheit and Celsius temperature scales is given by the linear function. F=95C+32F=\frac{9}{5} C+32F=59​C+32 Complete the table and find the slope. 12 -19 slope

Find f∘g∘hf \circ g \circ hf∘g∘h if f(x)=1x,g(x)=2x2+7, and h(x)=cos⁡xf(x)=\frac{1}{x}, \quad g(x)=2 x^{2}+7, \quad \text { and } \quad h(x)=\cos xf(x)=x1​,g(x)=2x2+7, and h(x)=cosx

Solve each equation for x. (a) ln⁡x=6\ln x=6lnx=6 (b) eex=5e^{e^{x}}=5eex=5

Use the Law of Exponents to rewrite and simplify the expression. x4x⋅x5x+1xx−5\frac{x^{4 x} \cdot x^{5 x+1}}{x^{x-5}}xx−5x4x⋅x5x+1​

Find the range of the function. y=5+cos⁡xy=5+\cos xy=5+cosx

Find all solutions of the equation correct to two decimal places. x3−9x2−40=0x^{3}-9 x^{2}-40=0x3−9x2−40=0

The graphs of f(x)f(x)f(x) and g(x)g(x)g(x) are given. For what values of x is f(x)=g(x)f(x)=g(x)f(x)=g(x) ?

Express the function in the form of f∘gf \circ gf∘g . v(t)=sec⁡(t4)tan⁡(t4)v(t)=\sec \left(t^{4}\right) \tan \left(t^{4}\right)v(t)=sec(t4)tan(t4) __________

If f(x)=4x2+2f(x)=4 x^{2}+2f(x)=4x2+2 , find and simplify f(1+h)−f(1)h\frac{f(1+h)-f(1)}{h}hf(1+h)−f(1)​ , where h≠0h \neq 0h=0 .

Find the solutions of the equation csc⁡(2θ)=1\csc (2 \theta)=1csc(2θ)=1 in [0,2π)[0,2 \pi)[0,2π) .

Simplify the expression. e3ln⁡5e^{3 \ln 5}e3ln5

A stone is dropped into a lake, creating a circular ripple that travels outward at a speed of 45 cm/s. Express the radius r of this circle as a function of the time t (in seconds) and find A∘rA \circ rA∘r if A is the area of this circle as a function of the radius.

What is x10\sqrt[10]{x}10x​ , given that H=f∘g∘hH=f \circ g \circ hH=f∘g∘h and H(x)=x−310H(x)=\sqrt[10]{\sqrt{x}-3}H(x)=10x​−3​ ?

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

Find the exponential function $f(x)=C a^{x}$ whose graph is given. $Find the exponential function f(x)=C a^{x} whose graph is given.$

If $f(x)=x^{2}-x+6$ , evaluate the difference quotient $\frac{f(a+h)-f(a)}{h}$ .

The function $f(x)=\sqrt{5+c x^{2}}$ is graphed below. $The function f(x)=\sqrt{5+c x^{2}} is graphed below.$

The relationship between the Fahrenheit and Celsius temperature scales is given by the linear function. $F=\frac{9}{5} C+32$ Complete the table and find the slope. 12 -19 slope

Find $f \circ g \circ h$ if $f(x)=\frac{1}{x}, \quad g(x)=2 x^{2}+7, \quad \text { and } \quad h(x)=\cos x$

Solve each equation for x. (a) $\ln x=6$ (b) $e^{e^{x}}=5$

Use the Law of Exponents to rewrite and simplify the expression. $\frac{x^{4 x} \cdot x^{5 x+1}}{x^{x-5}}$

Find the range of the function. $y=5+\cos x$

Find all solutions of the equation correct to two decimal places. $x^{3}-9 x^{2}-40=0$

The graphs of $f(x)$ and $g(x)$ are given. For what values of x is $f(x)=g(x)$ ?

Express the function in the form of $f \circ g$ . $v(t)=\sec \left(t^{4}\right) \tan \left(t^{4}\right)$ __________

If $f(x)=4 x^{2}+2$ , find and simplify $\frac{f(1+h)-f(1)}{h}$ , where $h \neq 0$ .

Find the solutions of the equation $\csc (2 \theta)=1$ in $[0,2 \pi)$ .

Simplify the expression. $e^{3 \ln 5}$

A stone is dropped into a lake, creating a circular ripple that travels outward at a speed of 45 cm/s. Express the radius r of this circle as a function of the time t (in seconds) and find $A \circ r$ if A is the area of this circle as a function of the radius.

What is $\sqrt[10]{x}$ , given that $H=f \circ g \circ h$ and $H(x)=\sqrt[10]{\sqrt{x}-3}$ ?