Exam 1: Functions, Graphs, and Limits

Two jets bound for San Diego leave Boston 20 minutes apart. The first travels at 450 miles per hour, while the second goes 500 miles per hour. How how many hours after the second plane departs will the second plane pass the first?

Find the points of intersection (if any) of the given pair of curves. $y = x ^ { 2 }$ and y = 3x - 2.

A closed box with a square base is to have a volume of 20 cubic meters. The material for the top and bottom of the box costs $3 per square meter, and the material for the sides costs $1 per square meter. Express the construction cost of the box as a function of the length of its base, x.

Determine the domain of the given function. $f ( x ) = \frac { x ^ { 2 } - 16 } { x + 1 }$

List all values of x for which f (x) is not continuous. $f ( x ) = \frac { 6 x + 6 } { x ^ { 2 } }$

Determine the domain of the given function. $f ( x ) = \sqrt { 2 x - 3 }$

Find all values of x for which the given function is not continuous. $f ( x ) = \frac { x ^ { 2 } + 3 x + 2 } { x ^ { 2 } + 4 x + 3 }$

Decide if the given function is continuous at the specified value of x. $f ( x ) = \left\{ \begin{array} { r l } x + 5 & \text { if } x < 1 \\3 x + 3 & \text { if } x \geq 1\end{array} ; \quad x = 1 \right.$

List all values of x for which f (x) is not continuous. $f ( x ) = \frac { 5 x + 1 } { x ^ { 2 } }$

Find the slope of the line with the following equation 9x + 4y = -8.

Find the distance between the given points.(-2, 6) and (3, 7)

Compute the indicated value of the given function. $f ( x ) = 2 x ^ { 2 } - x$ ; f (-1)

Find the points of intersection (if any) of the given pair of curves. y = 3x - 1 and y = 3 - 5x

Determine the domain of the given function. $f ( x ) = \frac { x ^ { 2 } - 1 } { x + 3 }$

Find the indicated one-sided limit. If the limiting value is infinite, indicate whether it is + $\infty$ or - $\infty$ . $\lim _ { x \rightarrow 2 ^ { - } } f ( x )$ where $f ( x ) = \left\{ \begin{aligned}x + 5 & \text { if } x < 2 \\x ^ { 2 } & \text { if } x \geq 2\end{aligned} \right.$

Find the slope and y-intercept (if they exist) of the line 2y = 9x.

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?

Compute the indicated value of the given function. $f ( x ) = 5 x ^ { 2 } - 3$ ; f (-1)

Determine the domain of the given function. $f ( x ) = \frac { x ^ { 2 } - 25 } { x + 2 }$

Find the slope (if possible) of the line that passes through the given pair of points. (19, 10) and (5, 8).