Exam 1: Functions and Their Graphs

Graph the function. - $f ( x ) = \left\{ \begin{array} { l l } 1 & \text { if } - 1 \leq x < 3 \\| x | & \text { if } 3 \leq x < 9 \\\sqrt { x } & \text { if } 9 \leq x \leq 11\end{array} \right.$ A) B) C) D)

Match the graph to the function listed whose graph most resembles the one given. -

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

Locate any intercepts of the function. - $f ( x ) = \left\{ \begin{array} { l l } 1 & \text { if } - 7 \leq x < - 7 \\| x | & \text { if } - 7 \leq x < 7 \\\sqrt [ 3 ] { x } & \text { if } 7 \leq x \leq 26\end{array} \right.$

The graph of a piecewise-defined function is given. Write a definition for the function. - A) $f ( x ) = \left\{ \begin{array} { l l } - \frac { 1 } { 2 } x & \text { if } - 4 < x < 0 \\ x & \text { if } 0 < x < 3 \end{array} \right.$ B) $f ( x ) = \left\{ \begin{array} { l l } - \frac { 1 } { 2 } x & \text { if } - 4 \leq x \leq 0 \\ x & \text { if } 0 < x \leq 3 \end{array} \right.$ C) $f ( x ) = \left\{ \begin{array} { l l } \frac { 1 } { 2 } x & \text { if } - 4 < x < 0 \\ x & \text { if } 0 < x < 3 \end{array} \right.$ D) $f ( x ) = \left\{ \begin{array} { l l } - 2 x & \text { if } - 4 \leq x \leq 0 \\ x & \text { if } 0 < x \leq 3 \end{array} \right.$

Find and simplify the difference quotient of f, $\frac { f ( x + h ) - f ( x ) } { h }$ $\mathbf { h } \neq 0$ , for the function. - $f ( x ) = x ^ { 2 } + 3 x + 7$

For the function, find the average rate of change of f from 1 to x: $\frac { f ( x ) - f ( 1 ) } { x - 1 } , x \neq 1$ - $f ( x ) = \sqrt { x + 35 }$

Write the word or phrase that best completes each statement or answers the question. -The wind chill factor represents the equivalent air temperature at a standard wind speed that would produce the same heat loss as the given temperature and wind speed. One formula for computing the equivalent temperature is $W ( t ) = \left\{ \begin{array} { l l } t & \text { if } 0 \leq v < 1.79 \\33 - \frac { ( 10.45 + 10 \sqrt { v } - v ) ( 33 - t ) } { 22.04 } & \text { if } 1.79 \leq \mathrm { v } < 20 \\33 - 1.5958 ( 33 - t ) & \text { if } v \geq 20\end{array} \right.$ where v represents the wind speed (in meters per second) and t represents the air temperature (°C). Compute the wind chill for an air temperature of 15°C and a wind speed of 12 meters per second. (Round the answer to one decimal place.)

Choose the one alternative that best completes the statement or answers the question. Graph the function by starting with the graph of the basic function and then using the techniques of shifting, compressing, stretching, and/or reflecting. - $f(x)=\sqrt{x}-5$ A) B) C) D)

Solve. -The amount of paint needed to cover the walls of a room varies jointly as the perimeter of the room and the height of the wall. If a room with a perimeter of 60 feet and 6-foot walls requires 3.6 quarts of paint, find the Amount of paint needed to cover the walls of a room with a perimeter of 45 feet and 6-foot walls.

Solve. -The power that a resistor must dissipate is jointly proportional to the square of the current flowing through the resistor and the resistance of the resistor. If a resistor needs to dissipate 20 watts of power when 2 amperes of Current is flowing through the resistor whose resistance is 5 ohms, find the power that a resistor needs to Dissipate when 4 amperes of current are flowing through a resistor whose resistance is 7 ohms.

Graph the function by starting with the graph of the basic function and then using the techniques of shifting, compressing, stretching, and/or reflecting. - $f(x)=\frac{7}{x}$

Determine whether the equation defines y as a function of x. - $y=x^{4}$

Answer the question about the given function. -Given the functi $f ( x ) = - 2 x ^ { 2 } - 4 x + 3$ , is the point (-2, -1) on the graph of f?

Solve the problem. -The price p and the quantity x sold of a certain product obey the demand equation: $p = - \frac { 1 } { 5 } x + 200 , \{ x \mid 0 \leq x \leq 500 \}$ What is the revenue to the nearest dollar when 300 units are sold?

Use a graphing utility to graph the function over the indicated interval and approximate any local maxima and local minima. If necessary, round answers to two decimal places. - $f ( x ) = x ^ { 3 } - 12 x + 2 ; ( - 5,5 )$

Use a graphing utility to graph the function over the indicated interval and approximate any local maxima and local minima. Determine where the function is increasing and where it is decreasing. If necessary, round answers to two decimal places. - $f ( x ) = x ^ { 3 } - 4 x ^ { 2 } + 6 ; ( - 1,4 )$

Solve the problem. -Elissa wants to set up a rectangular dog run in her backyard. She has 24 feet of fencing to work with and wants to use it all. If the dog run is to be x feet long, express the area of the dog run as a function of x. A) $A ( x ) = 11 x - x ^ { 2 }$ B) $A ( x ) = 13 x - x ^ { 2 }$ C) $A ( x ) = 14 x ^ { 2 } - x$ D) $A ( x ) = 12 x - x ^ { 2 }$

Choose the one alternative that best completes the statement or answers the question. Graph the function by starting with the graph of the basic function and then using the techniques of shifting, compressing, stretching, and/or reflecting. - $f(x)=|x|+1$ A) B) C) D)

Choose the one alternative that best completes the statement or answers the question. Graph the function by starting with the graph of the basic function and then using the techniques of shifting, compressing, stretching, and/or reflecting. - $f(x)=\sqrt{x-4}-3$ A) B) C) D)