Exam 1: Functions, Graphs, and Limits

Each unit of a certain commodity costs p = 43x + 96 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.

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

Find the indicated one-sided limit. If the limiting value is infinite, indicate whether it is + $\infty$ or - $\infty$ . $\lim _ { x \rightarrow 9 ^ { - } } \frac { \sqrt { x } - 3 } { x - 9 }$

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

The cost of renting a backhoe at one distributor is $335, plus $35 per day. Write a linear function C(x) that describes the cost of renting the backhoe for x days, then use your function to find how much it would cost to rent it for 7 days.

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) = (4 - x)(x + 5)

Write an equation for the line through (3, 0) with slope 2.

Determine the domain of the given function. $f ( t ) = \frac { \sqrt { t ^ { 2 } - 4 } } { t - 6 }$

If an object is thrown vertically upward with an initial speed of 128 ft/sec, its height (in feet) t seconds later is given by $H ( t ) = - 16 t ^ { 2 } + 128 t$ . Graph the function H(t) and use the graph to determine when the object will hit the ground.

The cost of renting a backhoe at one distributor is $335, plus $50 per day. Write a linear function C(x) that describes the cost of renting the backhoe for x days, then use your function to find how much it would cost to rent it for 18 days.

Find the slope (if possible) of the line that passes through the given pair of points. (6, 7) and (9, -1).

Complete the table by evaluating f (x) at the specified values of x. Then use the table to estimate the indicated limit, or show that it does not exist. $f ( x ) = \frac { 3 x + 5 } { x - 4 } ; \quad \lim _ { x \rightarrow 4 } f ( x )$ x 3.9 3.99 3.999 4 4.001 4.01 4.1 f(x) \times

Find the difference quotient, $\frac { f ( x + h ) - f ( x ) } { h }$ . $f ( x ) = \frac { 7 } { x }$

Find the slope and y-intercept of the line whose equation is given. y = 2x - 5.

Find the slope of the line passing through (4, 3) and (0, 4). Round your answer to two decimal places, if necessary.

To study the rate at which animals learn, a psychology student performed an experiment in which a rat was sent repeatedly through a laboratory maze. Suppose the time required for the rat to traverse the maze on the nth trial was approximately $T ( n ) = 5 + \frac { 2 } { n } - \frac { 4 } { n ^ { 2 } }$ minutes. How many minutes does it take the rat to traverse the maze on the 2nd trial?

Plot the given point in a rectangular coordinate system. (4, -5)

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 difference quotient, $\frac { f ( x + h ) - f ( x ) } { h }$ . $f ( x ) = \frac { 9 } { x }$

Find the indicated limit if it exists. $\lim _ { x \rightarrow 2 } \frac { x - 2 } { x ^ { 2 } - 4 }$