Question 1

Sketch the graph of the given function. $f ( x ) = x ^ { 2 } + 2$ (Tick marks are spaced one unit apart.)

Accepted Answer

A)  
 
B)  
 
C)  
 
D)

Question 2

Write an equation for the line with the given properties. Through (3, -1) with slope 2

Accepted Answer

The answer of Write an equation for the line with...

Question 3

Compute the indicated value of the given function. $$f ( t ) = \left\{ \begin{aligned}
- 3 t + 5 & \text { if } t < - 1 \
t ^ { 2 } + 6 & \text { if } t \geq - 1
\end{aligned} \right.$$ ; f (-3)

Accepted Answer

A)  14 
B)  -4 
C)  15 
D)  -3

Question 4

Find the indicated one-sided limit. If the limiting value is infinite, indicate whether it is +$\infty$or -$\infty$. $$\lim _ { x \rightarrow 36 ^ { - } } \frac { \sqrt { x } - 6 } { x - 36 }$$

Accepted Answer

The answer of Find the indicated one-sided limit. If the...

Question 5

Find the indicated limit if it exists. $\lim _ { x \rightarrow 1 } \left( 2 x ^ { 2 } - 3 x + 1 \right)$

Accepted Answer

The answer of Find the indicated limit if it exists....

Question 6

Compute the indicated value of the given function. $$f ( x ) = \left\{ \begin{aligned}
x ^ { 2 } - 1 & \text { if } x < 1 \
3 & \text { if } x = 1 \
2 - 5 x & \text { if } x > 1
\end{aligned} \right.$$ ; f (2)

Accepted Answer

The answer of Compute the indicated value of the given...

Question 7

A manufacturer's total cost consists of a fixed overhead of $350 plus production costs of $60 per unit. Express the total cost in dollars as a function of the number of units produced.

Accepted Answer

The answer of A manufacturer's total cost consists of a...

Question 8

Compute the indicated value of the given function. f (x) = | x + 2 | + 3| x - 1 |; f (-3)

Accepted Answer

A)  13 
B)  -133 
C)  9 
D)  23

Question 9

An appliance manufacturer can sell refrigerators for $600 apiece. The manufacturer's total cost consists of a fixed overhead of $12,000 plus production cost of $400 per refrigerator. How many refrigerators must be sold for the manufacturer to break even?

Accepted Answer

The answer of An appliance manufacturer can sell refrigerators for...

Question 10

Determine the domain of the given function. $$f ( x ) = x ^ { 4 } + 5 x ^ { 3 } + 4 x + 1$$

Accepted Answer

The answer of Determine the domain of the given function....

Question 11

List all the values of x for which the given function is not continuous. $$f ( x ) = \left\{ \begin{aligned}
x ^ { 2 } & \text { if } x \leq 2 \
4 & \text { if } x > 2
\end{aligned} \right.$$

Accepted Answer

The answer of List all the values of x for...

Question 12

Each unit of a certain commodity costs p = 11x + 12 cents when x units of the commodity are produced. If all units are sold at this price, express the revenue derived from the sales as a function of x.

Accepted Answer

A)  x(11x + 12) cents 
B)  10x + 12 cents 
C)  $11 x ^ { 2 } + 12$ cents 
D)  12x + 12 cents

Question 13

$$\lim _ { x \rightarrow 3 ^ {- } } f ( x ) = 3$$ where $$f ( x ) = \left\{ \begin{aligned}
x & \text { if } x < 3 \
x + 1 & \text { if } x \geq 3
\end{aligned} \right.$$

Accepted Answer

A) True 
 B)False

Question 14

Find the indicated limit if it exists. $\lim _ { x \rightarrow 1 } \frac { x ^ { 2 } + 3 x + 2 } { x ^ { 2 } - 1 }$

Accepted Answer

A)  $\frac { 3 } { 2 }$ 
B)  3 
C)  6 
D)  Does not exist

Exam 1: Functions, Graphs, and Limits

Sketch the graph of the given function. $f ( x ) = x ^ { 2 } + 2$ (Tick marks are spaced one unit apart.)

Write an equation for the line with the given properties. Through (3, -1) with slope 2

Compute the indicated value of the given function. $f ( t ) = \left\{ \begin{aligned}- 3 t + 5 & \text { if } t < - 1 \\t ^ { 2 } + 6 & \text { if } t \geq - 1\end{aligned} \right.$ ; f (-3)

Find the indicated one-sided limit. If the limiting value is infinite, indicate whether it is + $\infty$ or - $\infty$ . $\lim _ { x \rightarrow 36 ^ { - } } \frac { \sqrt { x } - 6 } { x - 36 }$

Find the indicated limit if it exists. $\lim _ { x \rightarrow 1 } \left( 2 x ^ { 2 } - 3 x + 1 \right)$

Compute the indicated value of the given function. $f ( x ) = \left\{ \begin{aligned}x ^ { 2 } - 1 & \text { if } x < 1 \\3 & \text { if } x = 1 \\2 - 5 x & \text { if } x > 1\end{aligned} \right.$ ; f (2)

A manufacturer's total cost consists of a fixed overhead of $350 plus production costs of $60 per unit. Express the total cost in dollars as a function of the number of units produced.

Compute the indicated value of the given function. f (x) = | x + 2 | + 3| x - 1 |; f (-3)

An appliance manufacturer can sell refrigerators for $600 apiece. The manufacturer's total cost consists of a fixed overhead of $12,000 plus production cost of $400 per refrigerator. How many refrigerators must be sold for the manufacturer to break even?

Determine the domain of the given function. $f ( x ) = x ^ { 4 } + 5 x ^ { 3 } + 4 x + 1$

List all the values of x for which the given function is not continuous. $f ( x ) = \left\{ \begin{aligned}x ^ { 2 } & \text { if } x \leq 2 \\4 & \text { if } x > 2\end{aligned} \right.$

Each unit of a certain commodity costs p = 11x + 12 cents when x units of the commodity are produced. If all units are sold at this price, express the revenue derived from the sales as a function of x.

$\lim _ { x \rightarrow 3 ^ {- } } f ( x ) = 3$ where $f ( x ) = \left\{ \begin{aligned}x & \text { if } x < 3 \\x + 1 & \text { if } x \geq 3\end{aligned} \right.$

Find the indicated limit if it exists. $\lim _ { x \rightarrow 1 } \frac { x ^ { 2 } + 3 x + 2 } { x ^ { 2 } - 1 }$

Exam 1: Functions, Graphs, and Limits

Sketch the graph of the given function. f(x) =x2+2f ( x ) = x ^ { 2 } + 2f(x) =x2+2 (Tick marks are spaced one unit apart.)

Write an equation for the line with the given properties. Through (3, -1) with slope 2

Compute the indicated value of the given function. f(t) ={−3t+5 if t<−1t2+6 if t≥−1f ( t ) = \left\{ \begin{aligned}- 3 t + 5 & \text { if } t < - 1 \\t ^ { 2 } + 6 & \text { if } t \geq - 1\end{aligned} \right.f(t) ={−3t+5t2+6​ if t<−1 if t≥−1​ ; f (-3)

Find the indicated one-sided limit. If the limiting value is infinite, indicate whether it is + ∞\infty∞ or - ∞\infty∞ . lim⁡x→36−x−6x−36\lim _ { x \rightarrow 36 ^ { - } } \frac { \sqrt { x } - 6 } { x - 36 }limx→36−​x−36x​−6​

Find the indicated limit if it exists. lim⁡x→1(2x2−3x+1)\lim _ { x \rightarrow 1 } \left( 2 x ^ { 2 } - 3 x + 1 \right)limx→1​(2x2−3x+1)

A manufacturer's total cost consists of a fixed overhead of $350 plus production costs of $60 per unit. Express the total cost in dollars as a function of the number of units produced.

Compute the indicated value of the given function. f (x) = | x + 2 | + 3| x - 1 |; f (-3)

An appliance manufacturer can sell refrigerators for $600 apiece. The manufacturer's total cost consists of a fixed overhead of $12,000 plus production cost of $400 per refrigerator. How many refrigerators must be sold for the manufacturer to break even?

Determine the domain of the given function. f(x)=x4+5x3+4x+1f ( x ) = x ^ { 4 } + 5 x ^ { 3 } + 4 x + 1f(x)=x4+5x3+4x+1

List all the values of x for which the given function is not continuous. f(x)={x2 if x≤24 if x>2f ( x ) = \left\{ \begin{aligned}x ^ { 2 } & \text { if } x \leq 2 \\4 & \text { if } x > 2\end{aligned} \right.f(x)={x24​ if x≤2 if x>2​

Each unit of a certain commodity costs p = 11x + 12 cents when x units of the commodity are produced. If all units are sold at this price, express the revenue derived from the sales as a function of x.

lim⁡x→3−f(x)=3\lim _ { x \rightarrow 3 ^ {- } } f ( x ) = 3limx→3−​f(x)=3 where f(x)={x if x<3x+1 if x≥3f ( x ) = \left\{ \begin{aligned}x & \text { if } x < 3 \\x + 1 & \text { if } x \geq 3\end{aligned} \right.f(x)={xx+1​ if x<3 if x≥3​

Find the indicated limit if it exists. lim⁡x→1x2+3x+2x2−1\lim _ { x \rightarrow 1 } \frac { x ^ { 2 } + 3 x + 2 } { x ^ { 2 } - 1 }limx→1​x2−1x2+3x+2​

Sketch the graph of the given function. $f ( x ) = x ^ { 2 } + 2$ (Tick marks are spaced one unit apart.)

Compute the indicated value of the given function. $f ( t ) = \left\{ \begin{aligned}- 3 t + 5 & \text { if } t < - 1 \\t ^ { 2 } + 6 & \text { if } t \geq - 1\end{aligned} \right.$ ; f (-3)

Find the indicated one-sided limit. If the limiting value is infinite, indicate whether it is + $\infty$ or - $\infty$ . $\lim _ { x \rightarrow 36 ^ { - } } \frac { \sqrt { x } - 6 } { x - 36 }$

Find the indicated limit if it exists. $\lim _ { x \rightarrow 1 } \left( 2 x ^ { 2 } - 3 x + 1 \right)$

Determine the domain of the given function. $f ( x ) = x ^ { 4 } + 5 x ^ { 3 } + 4 x + 1$

List all the values of x for which the given function is not continuous. $f ( x ) = \left\{ \begin{aligned}x ^ { 2 } & \text { if } x \leq 2 \\4 & \text { if } x > 2\end{aligned} \right.$

$\lim _ { x \rightarrow 3 ^ {- } } f ( x ) = 3$ where $f ( x ) = \left\{ \begin{aligned}x & \text { if } x < 3 \\x + 1 & \text { if } x \geq 3\end{aligned} \right.$

Find the indicated limit if it exists. $\lim _ { x \rightarrow 1 } \frac { x ^ { 2 } + 3 x + 2 } { x ^ { 2 } - 1 }$