Exam 2: Functions and Relations

Evaluate the function for the indicated value. -Evaluate $f ( - 1 )$ $f ( x ) = \left\{ \begin{array} { c c } 7 & x \leq - 2 \\| x + 1 | & - 2 < x \leq 2 \\- 5 & x > 2\end{array} \right.$

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

Find the exact distance between the points. - $( \sqrt { 5 } , - \sqrt { 3 } )$ and $( 4 \sqrt { 5 } , - 7 \sqrt { 3 } )$

Write the word or phrase that best completes each statement or answers the question. Provide the missing information. -A function f is a linear function if $f ( x ) =$ where m represents the slope and (0, b) represents the y-intercept.

Solve the problem. -Consider the function $f = \{ ( - 6 , - 3 ) , ( - 2,3 ) , ( 2 , - 1 ) , ( 4,2 ) \}$ Determine $f ( - 2 )$

Write a function based on the given parent function and the transformations in the given order. -Parent function $y = | x |$ 1. Shift $4.5$ units to the right. 2. Shrink horizontally by a factor of $\frac { 1 } { 5 }$ . 3. Reflect across the $y$ -axis.

Use the graph to solve the equation and inequality. Write the solution to the inequality in interval notation. -a. $3 x - 1 = 2 x - 2$ b. $3 x - 1 < 2 x - 2$

Determine the slope of the line passing through the given points. - $( 8 , - 1 )$ and $( 10 , - 7 )$

Write the word or phrase that best completes each statement or answers the question. Provide the missing information. -If the graph of a set of points (x, y) has two points aligned vertically then the relation (does/does not) define y as a function of x.

Write the word or phrase that best completes each statement or answers the question. Provide the missing information. -The expression represents the greatest integer, less than or equal to x.

Sketch the graph using transformations of a parent function (without a table of values). - $r ( x ) = \sqrt { x } + 2$

Write the word or phrase that best completes each statement or answers the question. Provide the missing information. -A graph of an equation is symmetric with respect to the if replacing x by -x and y by -y results in an equivalent equation.

An isosceles triangle is shown. Find the area of the triangle. Assume that the units shown in the grid are in meters. -

Solve the problem. -In 2005, a special mixed-nut blend at a store cost $1.35 per lb, and in 2010 the blend cost $1.83 per lb. Let y represent the cost of a pound of the mixed-nut blend x years after 2005. Use a Linear equation model to estimate the cost of a pound of the mixed-nut blend in 2007.

Solve the problem. -A pediatrician records the age x (in yr) and average height y (in inches) for girls between the ages of 2 and 10. a. Use the points $( 2,37 )$ and $( 6,50 )$ to write a linear model for these data. b. Use the model to forecast the average height of 11 -yr-old girls.

Determine the slope of the line passing through the given points. - $( 3 \sqrt { 11 } , 6 \sqrt { 6 } )$ and $( \sqrt { 11 } , \sqrt { 6 } )$

Solve the problem. -The position of an object in a video game is represented by an ordered pair. The coordinates of the ordered pair give the number of pixels horizontally and vertically from the origin. a. Suppose that player A is located at $( 54,337 )$ and player B is located at $( 414,63 )$ . How far apart are the players? Round to the nearest pixel. b. If the two players move directly toward each other at the same speed, where will they meet?

Find the indicated function and write its domain in interval notation. - $f ( x ) = \frac { 9 } { x ^ { 2 } - 11 } , g ( x ) = \sqrt { 4 - x } , ( f \circ g ) ( x ) = ?$

Use transformations to graph the given function. - $f ( x ) = | 4 x |$

Match the function with the graph. -