Exam 1: Functions and Their Graphs

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

Find the average rate of change for the function between the given values. - $f ( x ) = - 3 x ^ { 2 } - x$ ; from 5 to 6

Find the average rate of change for the function between the given values. - $f ( x ) = x ^ { 2 } + 6 x ;$ from 3 to 7

The graph of a function f is given. Use the graph to answer the question. -For what numbers $x$ is $f ( x ) < 0$ ?

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

Determine algebraically whether the function is even, odd, or neither. - $f ( x ) = \sqrt { x }$

The graph of a function is given. Decide whether it is even, odd, or neither. -

Determine whether the relation represents a function. If it is a function, state the domain and range. - $\{ ( - 4,11 ) , ( - 3,4 ) , ( 0 , - 5 ) , ( 3,4 ) , ( 5,20 ) \}$

Determine algebraically whether the function is even, odd, or neither. - $f ( x ) = \frac { - x ^ { 3 } } { 9 x ^ { 2 } + 7 }$

Using transformations, sketch the graph of the requested function. -The graph of a function $\mathrm { f }$ is illustrated. Use the graph of $\mathrm { f }$ as the first step toward graphing the function $\mathrm { F }$ ( $x$ ), where $\mathrm { F } ( \mathrm { x } ) = \mathrm { f } ( \mathrm { x } + 2 ) - 1$

Write the word or phrase that best completes each statement or answers the question. -A wire 20 feet long is to be cut into two pieces. One piece will be shaped as a square and the other piece will be shaped as an equilateral triangle. Express the total area A enclosed by the pieces of wire as a function of the length $x$ of a side of the equilateral triangle. What is the domain of $A$ ?

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. - $f(x)=|x-2|$

Find the value for the function. -Find $f ( 4 )$ when $f ( x ) = x ^ { 2 } - 4 x + 3$

Determine whether the relation represents a function. If it is a function, state the domain and range. -

Determine whether the relation represents a function. If it is a function, state the domain and range. - $\{ ( - 3,6 ) , ( 2,3 ) , ( 3 , - 3 ) , ( 8 , - 1 ) \}$

Solve. -The volume $\mathrm { V }$ of a given mass of gas varies directly as the temperature $\mathrm { T }$ and inversely as the pressure $\mathrm { P }$ . A measuring device is calibrated to give $\mathrm { V } = 319.2$ in $^ { 3 }$ when $\mathrm { T } = 570 ^ { \circ }$ and $\mathrm { P } = 25 \mathrm { lb } / \mathrm { in } ^ { 2 }$ . What is the volume on this device when the temperature is $430 ^ { \circ }$ and the pressure is $20 \mathrm { lb } / \mathrm { in } ^ { 2 }$ ?

Find the domain of the function. - $f ( x ) = \left\{ \begin{array} { l l } 2 x & \text { if } x \neq 0 \\2 & \text { if } x = 0\end{array} \right.$

The graph of a function is given. Determine whether the function is increasing, decreasing, or constant on the given interval. - $( 1,5 )$

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

The graph of a function is given. Decide whether it is even, odd, or neither. -