Exam 1: Functions and Their Graphs

Determine whether the function has an inverse function.If it does, find the inverse function. $f ( x ) = \left\{ \begin{array} { l } 8 x + 13 , x < - 2 \\( x + 2 ) ^ { 2 } - 3 , x \geq - 2\end{array} \right.$

Evaluate the function h(x) = 2[[x]] for x = -4. ​

The total numbers of Navy personnel N (in thousands) and Marines personnel M (in thousands) from 2000 through 2007 can be approximated by the models $N ( t ) = 0.193 t ^ { 3 } - 3.88 t ^ { 2 } + 15.9 t + 370$ and $M ( t ) = 0.033 t ^ { 3 } - 0.21 t ^ { 2 } + 1.7 t + 171$ Where t represents the year, with t = 0 corresponding to 2000. Find and interpret $( N + M ) ( t )$ .

Use a graphing utility to graph the function and find the zeroes of the function. $f ( x ) = 7 - \frac { 3 } { x }$

Select the graph of the function and determine whether it is even, odd, or neither. ​ F(x) = x² - 6 ​

Evaluate f(-7) if f(x) = 12x - 8. ​

Find a mathematical model representing the statement.(Determine the constant of proportionality.) P varies directly as x and inversely as the square of y.(P = $\frac { 3 } { 2 }$ when x = 25 and y = 10.)

Find the y-intercept of the graph of the equation 4y = 3x + 12. ​

Select the correct graph of the given function. $f ( x ) = | x - 6 |$

Find the coordinates of a second point on the graph of a function f if the given point is on the graph and the function is odd. $\left( - \frac { 9 } { 7 } , - 4 \right)$

Find the x-intercept of the graph of the equation y = 3x + 15. ​

Select the correct graph of the given function. $f ( x ) = - 3 x ^ { 3 }$

Evaluate f(-4) if $f ( x ) = \left\{ \begin{array} { l } x ^ { 2 } + 5 , \quad x < 1 \\5 x ^ { 2 } + 5 , \quad x \geq 1\end{array} \right.$ .

The sales tax on an item with a retail price of $972 is $68.04.Create a variational model that gives the retail price, y, in terms of the sales tax, x, and use it to determine the retail price of an item that has a sales tax of $82.62.

Use algebraic tests to check the following for symmetry with respect to the axes and the origin. $3 x + 2 y ^ { 6 } = 0$

Plot the points in the Cartesian plane. $\left( 4 , - \frac { 1 } { 6 } \right) , \left( \frac { 5 } { 2 } , 5 \right) , ( - 3,3 ) , \left( \frac { 2 } { 5 } , - \frac { 2 } { 5 } \right)$

Find (f + g)(x). f(x)=-2x-1 g(x)=-3+x-1

Select the graph of the function. $f ( x ) = \left\{ \begin{array} { l l } 3 - x ^ { 2 } & x < 0 \\x ^ { 2 } + 2 & x \geq 0\end{array} \right.$

Evaluate the indicated function for $f ( x ) = x ^ { 2 } + 5$ and $g ( x ) = x - 2$ . $( f g ) ( 5 )$

Evaluate the function for the indicated values. f (x) = 5[[x + 3]] - 5 (i) f (3) (ii) f (-63.30) (iii) f ( $\frac { 7 } { 8 }$ )