Exam 1: Functions, Graphs, and Limits

Find the indicated one-sided limit. If the limiting value is infinite, indicate whether it is + $\infty$ or - $\infty$ . $\lim _ { x \rightarrow 1 ^ { + } } \frac { \sqrt { x - 1 } } { x - 1 }$

If f (x) is graphed below, find $\lim _ { x \rightarrow 1 } f ( x )$ if it exists.

Find the slope and y-intercept of the line whose equation is given. 5y = 8x

Find the distance between the given points.(-3, -2) and (5, 3)

Find the indicated limit if it exists. $\lim _ { x \rightarrow 1 } \left( 3 x ^ { 2 } - 8 x + 1 \right)$

Find all the values of x for which the given function is not continuous. $f ( x ) = \left\{ \begin{aligned}x ^ { 2 } + 4 & \text { if } x \leq 5 \\4 & \text { if } x > 5\end{aligned} \right.$

Find the composite function $f ( g ( x ) )$ $f ( u ) = u ^ { 3 } + 2 , g ( x ) = x + 3$

Find all the values of x for which the given function is not continuous. $f ( x ) = \left\{ \begin{aligned}x ^ { 2 } + 5 & \text { if } x \leq 5 \\2 & \text { if } x > 5\end{aligned} \right.$

Find the indicated composite function.f (x + 7) where $f ( x ) = \frac { 1 } { x }$

Two car rental agencies are competing. One agency rents cars for 50 dollars per day and 30 cents a mile; the other agency rents cars for 30 dollars per day and 50 cents a mile. For a 9 day trip, how many miles must you travel to have the total cost be the same with each agency? Round to the nearest whole mile , if necessary.

A rectangle is constructed inside a circle of radius r with the corners of the rectangle lying on the circle. Express the area A of the rectangle as a function of the radius r if the width of one side of the rectangle is 2.

List all values of x for which f (x) is not continuous. $f ( x ) = \frac { 10 x - 15 } { x - 5 }$

List all values of x for which f (x) is not continuous. $f ( x ) = \frac { 3 x + 3 } { x ^ { 2 } }$

Find $\lim _ { x \rightarrow + \infty } f ( x )$ and $\lim _ { x \rightarrow - \infty } f ( x )$ . If the limiting value is infinite indicate whether it is + $\infty$ or - $\infty$ . f (x) = (8 - 3x)(x + 4)

A farmer is planning to plant a rectangular garden with an area of 4,000 square yards. The garden is to be fenced on all four sides. Express the number of yards of fencing required as a function of x, the long side of the fence.

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

Two jets bound for San Diego leave Boston 20 minutes apart. The first plane travels at 300 miles per hour, while the second plane goes 320 miles per hour. At what time will the second plane pass the first?

What is the equation of the line through the points (7, -3) and (5, 19)? Round numbers to two decimal places, if necessary.

Find the slope and y-intercept (if they exist) of the line 2y = 7x.

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