Question 1

Let $f(x)=x^{2}-6 x+5$ and $g(x)=\sqrt{x+5}$ . Find $\left(g^{\circ} g\right)(20)$ .

Accepted Answer

The answer of Let $f(x)=x^{2}-6 x+5$ and $g(x)=\sqrt{x+5}$ . Find...

Question 2

Use the laws of logarithms to expand the expression. ln $\left(\frac{x+5}{x-6}\right)^{\frac{1}{2}}$

Accepted Answer

A)  $\frac{1}{2}$ ln $\left(x-\frac{5}{6}\right)$ 
B)  $\frac{1}{2}$ ln [(x + 5)(x - 6)] 
C)  $\frac{1}{2}$ ln $\left(\frac{x+5}{x-6}\right)$ 
D)  $\frac{1}{2}$ ln (x + 5) - $\frac{1}{2}$ ln (x - 6) 
A)  $\frac{1}{2}$ ln $\left(x-\frac{5}{6}\right)$ 
B)  $\frac{1}{2}$ ln [(x + 5)(x - 6)] 
C)  $\frac{1}{2}$ ln $\left(\frac{x+5}{x-6}\right)$ 
D)  $\frac{1}{2}$ ln (x + 5) - $\frac{1}{2}$ ln (x - 6)

Question 3

Find the exact value of the expression. $\log _{5} 20+\log _{5} 35-6 \log _{5} 2$

Accepted Answer

A)  4 
B)  3 
C)  1 
D)  5 
E)  2 
A)  4 
B)  3 
C)  1 
D)  5 
E)  2

Question 4

Which of the following graphs is neither even nor odd?

Accepted Answer

A)  $f(x)=\frac{4 x^{2}}{x^{4}+1}$ 
B)  $f(x)=8 x^{3}+10 x^{2}+1$ 
C)  $f(x)=x^{3}-9 x$ 
A)  $f(x)=\frac{4 x^{2}}{x^{4}+1}$ 
B)  $f(x)=8 x^{3}+10 x^{2}+1$ 
C)  $f(x)=x^{3}-9 x$

Question 5

Find a formula for the inverse of the function. $y=\ln (x+6)$

Accepted Answer

A)  $y=e^{x}-6$ 
B)  $y=e^{x}+6$ 
C)  $y=-6 e^{x}$ 
D)  $y=6 e^{x}$ 
E)  $y=e^{x+6}$ 
A)  $y=e^{x}-6$ 
B)  $y=e^{x}+6$ 
C)  $y=-6 e^{x}$ 
D)  $y=6 e^{x}$ 
E)  $y=e^{x+6}$

Question 6

Suppose that the graph of $y=\log _{2} x$ is drawn on a coordinate grid where the unit of measurement is an inch. How many miles to the right of the origin do we have to move before the height of the curve reaches 3 ft? Rounded to the nearest mile.

Accepted Answer

A)  13015052.4 mi 
B)  1084587.7 mi 
C)  13,014,952 mi 
D)  13,015,152 mi 
E)  5.2 mi 
A)  13015052.4 mi 
B)  1084587.7 mi 
C)  13,014,952 mi 
D)  13,015,152 mi 
E)  5.2 mi

Question 7

The graphs of $f(x)$ and $g(x)$ are given.
Find the values of $f(-4)$ and $g(3)$ .

Accepted Answer

The answer of The graphs of $f(x)$ and $g(x)$ are...

Question 8

Determine whether the function whose graph is given is even, odd, or neither.

Accepted Answer

A)  Even 
B)  Neither 
C)  Odd 
A)  Even 
B)  Neither 
C)  Odd

Question 9

Find the inverse of
f. Then sketch the graphs of f and $f^{-1}$ on the same set of axes.
f(x) = $\cos ^{-1}\left(\frac{x}{3}\right)$ , $-3 \leq x \leq 3$

Accepted Answer

The answer of Find the inverse of
f. Then sketch the...

Question 10

Find the inverse of F) Then sketch the graphs of f and $f^{-1}$ on the same set of axes. $f(x)=\sqrt{1-x^{2}}$ , $x \geq 0$

Accepted Answer

A)  $f^{-1}(x)=-\sqrt{1+x^{2}}$ , $x \geq 0$   
B)  $f^{-1}(x)=-\sqrt{1-x^{2}}$ , $x \geq 0$   
C)  $f^{-1}(x)=\sqrt{1-x^{2}}$ , $x \geq 0$   
D)  $f^{-1}(x)=\sqrt{1+x^{2}}$ , $x \geq 0$   
A)  $f^{-1}(x)=-\sqrt{1+x^{2}}$ , $x \geq 0$   
B)  $f^{-1}(x)=-\sqrt{1-x^{2}}$ , $x \geq 0$   
C)  $f^{-1}(x)=\sqrt{1-x^{2}}$ , $x \geq 0$   
D)  $f^{-1}(x)=\sqrt{1+x^{2}}$ , $x \geq 0$

Question 11

An open rectangular box with volume 2 $\mathrm{m}^{3}$ has a square base. Express the surface area of the box as a function $S(x)$ of the length $X$ of a side of the base.

Accepted Answer

A)  $S(x)=x^{2}+\frac{8}{x^{2}}$ 
B)  $S(x)=2 x^{2}+\frac{-2}{x^{2}}$ 
C)  $S(x)=x^{2}+\frac{-2}{x^{2}}$ 
D)  $S(x)=2 x+\frac{-2}{x}$ 
E)  $S(x)=x^{2}+\frac{8}{x}$ 
A)  $S(x)=x^{2}+\frac{8}{x^{2}}$ 
B)  $S(x)=2 x^{2}+\frac{-2}{x^{2}}$ 
C)  $S(x)=x^{2}+\frac{-2}{x^{2}}$ 
D)  $S(x)=2 x+\frac{-2}{x}$ 
E)  $S(x)=x^{2}+\frac{8}{x}$

Question 12

Find the inverse function of $f(x)=\frac{x+1}{2 x+1}$ .

Accepted Answer

A)  $f^{-1}(x)=-\frac{x-1}{2 x-1}$ 
B)  $f^{-1}(x)=\frac{x}{2 x-1}$ 
C)  $f^{-1}(x)=(x+1)(2 x+1)$ 
D)  $f^{-1}(x)=-\frac{2 x+1}{x-1}$ 
E)  $f^{-1}(x)=-(x+1)(2 x+1)$ 
A)  $f^{-1}(x)=-\frac{x-1}{2 x-1}$ 
B)  $f^{-1}(x)=\frac{x}{2 x-1}$ 
C)  $f^{-1}(x)=(x+1)(2 x+1)$ 
D)  $f^{-1}(x)=-\frac{2 x+1}{x-1}$ 
E)  $f^{-1}(x)=-(x+1)(2 x+1)$

Question 13

Starting with the graph of $y=e^{x}$ , write the equation of the graph that results from shifting 5 units right.

Accepted Answer

A)  $y=e^{x+5}$ 
B)  $y=e^{x}-5$ 
C)  $y=e^{x-5}$ 
D)  $y=e^{x}+5$ 
E)  $y=5 e^{x-5}$ 
A)  $y=e^{x+5}$ 
B)  $y=e^{x}-5$ 
C)  $y=e^{x-5}$ 
D)  $y=e^{x}+5$ 
E)  $y=5 e^{x-5}$

Question 14

If a bacteria population starts with 100 bacteria and doubles every three hours, then the number of bacteria after t hours is $n=f(t)=100\left(2^{\frac{t}{3}}\right)$ . When will the population reach 35,000? Round the answer to the nearest tenth.

Accepted Answer

A)  30.4 hours 
B)  15.4 hours 
C)  20.4 hours 
D)  35.4 hours 
E)  25.4 hours 
A)  30.4 hours 
B)  15.4 hours 
C)  20.4 hours 
D)  35.4 hours 
E)  25.4 hours

Question 15

Find the points of intersection of the graphs of the functions. Express your answers accurate to five decimal places. f (x) = 0.5 $x^{3}$ - 1.7 $x^{2}$ + 2.3x - 2; $g(x)$ = 2.8x - 4.8

Accepted Answer

A)  (-1.21519, -3.40253)
(1)46104, 8.83163)
(3)15415, 4.0909) 
B)  (-1.21519, -8.20253),
(3)15415, 4.03163) 
C)  (-1.21519, -8.20253),
(1)46104, -0.7091)
(3)15415, 4.03163) 
D)  (-1.21519, -3.40253)
(3)15415, 4.0909) 
A)  (-1.21519, -3.40253)
(1)46104, 8.83163)
(3)15415, 4.0909) 
B)  (-1.21519, -8.20253),
(3)15415, 4.03163) 
C)  (-1.21519, -8.20253),
(1)46104, -0.7091)
(3)15415, 4.03163) 
D)  (-1.21519, -3.40253)
(3)15415, 4.0909)

Question 16

Find the domain of the function. $f(x)=\sqrt{36-2 x^{2}}$

Accepted Answer

The answer of Find the domain of the function. \(f(x)=\sqrt{36-2...

Question 17

A spherical balloon with radius $r$ inches has volume $4 \frac{\pi r^{3}}{3}$ .
Find a function that represents the amount of air required to inflate the balloon from a radius of $4 \frac{\pi r^{3}}{3}$ inches to a radius of $r+3$ inches.

Accepted Answer

The answer of A spherical balloon with radius $r$ inches...

Question 18

The graph of the function $f$ follows. Choose the graph of $y=f\left(\frac{x}{2}\right)+1$

Accepted Answer

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

Question 19

By cutting away identical squares from each corner of a rectangular piece of cardboard and folding up the resulting flaps, an open box can be made. If the cardboard is 18 in. long and 9 in. wide and the square cutaways have dimensions of x in. by x in., find a function that gives the volume of the resulting box.

Accepted Answer

The answer of By cutting away identical squares from each...

Question 20

Scientists have discovered that a linear relationship exists between the amount of flobberworm mucus secretions and the air temperature. When the temperature is 65°F, the flobberworms each secrete 16 grams of mucus a day; when the temperature is 95°F, they each secrete 22 grams of mucus a day. Find a function M(t) that gives the amount of mucus secreted on a given day, where t is the temperature of that day in degrees Fahrenheit.

Accepted Answer

A)  $M(t)=0.2 t+16$ 
B)  $M(t)=5 t+16$ 
C)  $M(t)=5 t+3$ 
D)  $M(t)=0.2 t+3$ 
A)  $M(t)=0.2 t+16$ 
B)  $M(t)=5 t+16$ 
C)  $M(t)=5 t+3$ 
D)  $M(t)=0.2 t+3$

Let $f(x)=x^{2}-6 x+5$ and $g(x)=\sqrt{x+5}$ . Find $\left(g^{\circ} g\right)(20)$ .

Use the laws of logarithms to expand the expression. ln $\left(\frac{x+5}{x-6}\right)^{\frac{1}{2}}$

Find the exact value of the expression. $\log _{5} 20+\log _{5} 35-6 \log _{5} 2$

Which of the following graphs is neither even nor odd?

Find a formula for the inverse of the function. $y=\ln (x+6)$

Suppose that the graph of $y=\log _{2} x$ is drawn on a coordinate grid where the unit of measurement is an inch. How many miles to the right of the origin do we have to move before the height of the curve reaches 3 ft? Rounded to the nearest mile.

The graphs of $f(x)$ and $g(x)$ are given. Find the values of $f(-4)$ and $g(3)$ .

Determine whether the function whose graph is given is even, odd, or neither.

Find the inverse of f. Then sketch the graphs of f and $f^{-1}$ on the same set of axes. f(x) = $\cos ^{-1}\left(\frac{x}{3}\right)$ , $-3 \leq x \leq 3$

Find the inverse of F) Then sketch the graphs of f and $f^{-1}$ on the same set of axes. $f(x)=\sqrt{1-x^{2}}$ , $x \geq 0$

An open rectangular box with volume 2 $\mathrm{m}^{3}$ has a square base. Express the surface area of the box as a function $S(x)$ of the length $X$ of a side of the base.

Find the inverse function of $f(x)=\frac{x+1}{2 x+1}$ .

Starting with the graph of $y=e^{x}$ , write the equation of the graph that results from shifting 5 units right.

If a bacteria population starts with 100 bacteria and doubles every three hours, then the number of bacteria after t hours is $n=f(t)=100\left(2^{\frac{t}{3}}\right)$ . When will the population reach 35,000? Round the answer to the nearest tenth.

Find the points of intersection of the graphs of the functions. Express your answers accurate to five decimal places. f (x) = 0.5 $x^{3}$ - 1.7 $x^{2}$ + 2.3x - 2; $g(x)$ = 2.8x - 4.8

Find the domain of the function. $f(x)=\sqrt{36-2 x^{2}}$

A spherical balloon with radius $r$ inches has volume $4 \frac{\pi r^{3}}{3}$ . Find a function that represents the amount of air required to inflate the balloon from a radius of $4 \frac{\pi r^{3}}{3}$ inches to a radius of $r+3$ inches.

The graph of the function $f$ follows. Choose the graph of $y=f\left(\frac{x}{2}\right)+1$ $The graph of the function f follows. Choose the graph of y=f\left(\frac{x}{2}\right)+1$

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

Let f(x)=x2−6x+5f(x)=x^{2}-6 x+5f(x)=x2−6x+5 and g(x)=x+5g(x)=\sqrt{x+5}g(x)=x+5​ . Find (g∘g)(20)\left(g^{\circ} g\right)(20)(g∘g)(20) .

Use the laws of logarithms to expand the expression. ln (x+5x−6)12\left(\frac{x+5}{x-6}\right)^{\frac{1}{2}}(x−6x+5​)21​

Find the exact value of the expression. log⁡520+log⁡535−6log⁡52\log _{5} 20+\log _{5} 35-6 \log _{5} 2log5​20+log5​35−6log5​2

Which of the following graphs is neither even nor odd?

Find a formula for the inverse of the function. y=ln⁡(x+6)y=\ln (x+6)y=ln(x+6)

Suppose that the graph of y=log⁡2xy=\log _{2} xy=log2​x is drawn on a coordinate grid where the unit of measurement is an inch. How many miles to the right of the origin do we have to move before the height of the curve reaches 3 ft? Rounded to the nearest mile.

The graphs of f(x)f(x)f(x) and g(x)g(x)g(x) are given. Find the values of f(−4)f(-4)f(−4) and g(3)g(3)g(3) .

Determine whether the function whose graph is given is even, odd, or neither.

Find the inverse of f. Then sketch the graphs of f and f−1f^{-1}f−1 on the same set of axes. f(x) = cos⁡−1(x3)\cos ^{-1}\left(\frac{x}{3}\right)cos−1(3x​) , −3≤x≤3-3 \leq x \leq 3−3≤x≤3

Find the inverse of F) Then sketch the graphs of f and f−1f^{-1}f−1 on the same set of axes. f(x)=1−x2f(x)=\sqrt{1-x^{2}}f(x)=1−x2​ , x≥0x \geq 0x≥0

An open rectangular box with volume 2 m3\mathrm{m}^{3}m3 has a square base. Express the surface area of the box as a function S(x)S(x)S(x) of the length XXX of a side of the base.

Find the inverse function of f(x)=x+12x+1f(x)=\frac{x+1}{2 x+1}f(x)=2x+1x+1​ .

Starting with the graph of y=exy=e^{x}y=ex , write the equation of the graph that results from shifting 5 units right.

If a bacteria population starts with 100 bacteria and doubles every three hours, then the number of bacteria after t hours is n=f(t)=100(2t3)n=f(t)=100\left(2^{\frac{t}{3}}\right)n=f(t)=100(23t​) . When will the population reach 35,000? Round the answer to the nearest tenth.

Find the points of intersection of the graphs of the functions. Express your answers accurate to five decimal places. f (x) = 0.5 x3x^{3}x3 - 1.7 x2x^{2}x2 + 2.3x - 2; g(x)g(x)g(x) = 2.8x - 4.8

Find the domain of the function. f(x)=36−2x2f(x)=\sqrt{36-2 x^{2}}f(x)=36−2x2​

A spherical balloon with radius rrr inches has volume 4πr334 \frac{\pi r^{3}}{3}43πr3​ . Find a function that represents the amount of air required to inflate the balloon from a radius of 4πr334 \frac{\pi r^{3}}{3}43πr3​ inches to a radius of r+3r+3r+3 inches.

The graph of the function fff follows. Choose the graph of y=f(x2)+1y=f\left(\frac{x}{2}\right)+1y=f(2x​)+1

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

Let $f(x)=x^{2}-6 x+5$ and $g(x)=\sqrt{x+5}$ . Find $\left(g^{\circ} g\right)(20)$ .

Use the laws of logarithms to expand the expression. ln $\left(\frac{x+5}{x-6}\right)^{\frac{1}{2}}$

Find the exact value of the expression. $\log _{5} 20+\log _{5} 35-6 \log _{5} 2$

Find a formula for the inverse of the function. $y=\ln (x+6)$

Suppose that the graph of $y=\log _{2} x$ is drawn on a coordinate grid where the unit of measurement is an inch. How many miles to the right of the origin do we have to move before the height of the curve reaches 3 ft? Rounded to the nearest mile.

The graphs of $f(x)$ and $g(x)$ are given. Find the values of $f(-4)$ and $g(3)$ .

Find the inverse of f. Then sketch the graphs of f and $f^{-1}$ on the same set of axes. f(x) = $\cos ^{-1}\left(\frac{x}{3}\right)$ , $-3 \leq x \leq 3$

Find the inverse of F) Then sketch the graphs of f and $f^{-1}$ on the same set of axes. $f(x)=\sqrt{1-x^{2}}$ , $x \geq 0$

An open rectangular box with volume 2 $\mathrm{m}^{3}$ has a square base. Express the surface area of the box as a function $S(x)$ of the length $X$ of a side of the base.

Find the inverse function of $f(x)=\frac{x+1}{2 x+1}$ .

Starting with the graph of $y=e^{x}$ , write the equation of the graph that results from shifting 5 units right.

If a bacteria population starts with 100 bacteria and doubles every three hours, then the number of bacteria after t hours is $n=f(t)=100\left(2^{\frac{t}{3}}\right)$ . When will the population reach 35,000? Round the answer to the nearest tenth.

Find the points of intersection of the graphs of the functions. Express your answers accurate to five decimal places. f (x) = 0.5 $x^{3}$ - 1.7 $x^{2}$ + 2.3x - 2; $g(x)$ = 2.8x - 4.8

Find the domain of the function. $f(x)=\sqrt{36-2 x^{2}}$

A spherical balloon with radius $r$ inches has volume $4 \frac{\pi r^{3}}{3}$ . Find a function that represents the amount of air required to inflate the balloon from a radius of $4 \frac{\pi r^{3}}{3}$ inches to a radius of $r+3$ inches.

The graph of the function $f$ follows. Choose the graph of $y=f\left(\frac{x}{2}\right)+1$ $The graph of the function f follows. Choose the graph of y=f\left(\frac{x}{2}\right)+1$