Exam 1: Functions and Their Graphs

Solve. -The amount of water used to take a shower is directly proportional to the amount of time that the shower is in use. A shower lasting 17 minutes requires 10.2 gallons of water. Find the amount of water used in a shower Lasting 12 minutes.

Find an equation of the secant line containing (1, f(1)) and (2, f(2)). - $f ( x ) = x ^ { 3 } - x$

Solve the problem. - $f ( x ) = 5 x - 8$

Solve the problem. -Sue wants to put a rectangular garden on her property using 76 meters of fencing. There is a river that runs through her property so she decides to increase the size of the garden by using the river as one side of the rectangle. (Fencing is then needed only on the other three sides.) Let x represent the length of the side of the rectangle along the river. Express the garden's area as a function of $x$ .

For the graph of the function y = f(x), find the absolute maximum and the absolute minimum, if it exists. -

Graph the function by starting with the graph of the basic function and then using the techniques of shifting, compressing, stretching, and/or reflecting. - $f(x)=5|x|$

Graph the function. - $f(x)=3$

Based on the graph, find the range of y = f(x). - $f ( x ) = \left\{ \begin{array} { l l } 4 & \text { if } - 6 \leq x < - 2 \\| x | & \text { if } - 2 \leq x < 5 \\\sqrt [ 3 ] { x } & \text { if } 5 \leq x \leq 12\end{array} \right.$

Graph the function by starting with the graph of the basic function and then using the techniques of shifting, compressing, stretching, and/or reflecting. - $f(x)=\sqrt{-x}$

Solve the problem. -The gravitational attraction A between two masses varies inversely as the square of the distance between them. The force of attraction is 9 lb when the masses are 2 ft apart, what is the attraction when the masses are 6 ft Apart?

Choose the one alternative that best completes the statement or answers the question. -The concentration $\mathrm { C }$ (arbitrary units) of a certain drug in a patient's bloodstream can be modeled using $C ( t ) = \frac { t } { ( 0.423 t + 2.366 ) ^ { 2 } }$ , where $t$ is the number of hours since a 500 milligram oral dose was administered. Using the TABLE feature of a graphing utility, find the time at which the concentration of the drug is greatest. Round to the nearest tenth of an hour.

Determine whether the graph is that of a function. If it is, use the graph to find its domain and range, the intercepts, if any, and any symmetry with respect to the x-axis, the y-axis, or the origin. -

Solve the problem. -Express the gross salary $G$ of a person who earns $\$ 35$ per hour as a function of the number $x$ of hours worked.

Determine algebraically whether the function is even, odd, or neither. - $f ( x ) = 2 x ^ { 3 } - 4$

Solve the problem. -A wire of length $3 x$ is bent into the shape of a square. Express the area A of the square as a function of x.

For the given functions f and g, find the requested function and state its domain. - $f ( x ) = \sqrt { 6 - x } ; g ( x ) = \sqrt { x - 2 }$ Find $f \cdot g$ .

Graph the function. - $f(x)=\left\{\begin{array}{ll}-x+3 & \text { if } x<2 \\2 x-3 & \text { if } x \geq 2\end{array}\right.$

If y varies directly as x, find a linear function which relates them. - $y = 2 \text { when } x = \frac { 1 } { 9 }$

Solve. -The amount of gas that a helicopter uses is directly proportional to the number of hours spent flying. The helicopter flies for 2 hours and uses 18 gallons of fuel. Find the number of gallons of fuel that the helicopter uses To fly for 5 hours.

The graph of a function is given. Determine whether the function is increasing, decreasing, or constant on the given interval. - $( - 4,1 )$