Exam 2: Functions and Relations

Write the word or phrase that best completes each statement or answers the question. Provide the missing information. -A equation in the variables x and y can be written in the form Ax + By = C, where A and B are not both zero.

Determine if the given points form the vertices of a right triangle. -(-3, 5), (-1, 3), and (-4, 0)

Determine which of the given points are solutions to the given equation. - $2 x ^ { 2 } + y = 4$ I. $( 3 , - 14 )$ II. $( - 3,14 )$ III. $( - 3 , - 14 )$

Graph the equation with a graphing utility on the given viewing window. - $y = 3 x - 5 \text { on } [ - 10,10,1 ] \text { by } [ - 10,10,1 ]$

Graph the function. - $s ( x ) = \left\{ \begin{array} { l l } - x + 3 & \text { for } x \leq 3 \\ \sqrt { x - 3 } & \text { for } x > 3 \end{array} \right.$

Write the word or phrase that best completes each statement or answers the question. Provide the missing information. -An equation of a circle written in the form $x ^ { 2 } + y ^ { 2 } + A x + B y + C = 0$ = 0 is called the form of an equation of a circle.

Identify the domain and range of the relation, and determine whether the relation is a function. - $\{ ( - 9,4 ) , ( - 1,2 ) , ( 18 , - 2 ) , ( - 1 , - 4 ) \}$

Write the domain in interval notation. - $h ( c ) = \frac { 2 } { \sqrt { c + 11 } - 1 }$

Assume that the units shown in the grid are in feet. a. Determine the exact length and width of the rectangle shown. b. Determine the perimeter and area. -

Evaluate the function for the given value of x. - $g ( x ) = 4 x - 3 , h ( x ) = 3 \sqrt { x - 7 } , ( h \circ g ) ( 1 ) =$ ?

Find the indicated function and write its domain in interval notation. - $n ( x ) = x + 3 , q ( x ) = \frac { 1 } { x + 6 } , ( q \circ n ) ( x ) = ?$

The graph of y = f (x) is given. Graph the indicated function. -Graph $y = - f ( x - 2 ) - 2$

Choose the one alternative that best completes the statement or answers the question. -If bottled water costs $0.63 per bottle, then the cost, C (in dollars), for b bottles is defined by C(b) = 0.63b. How many bottles of water can be purchased for $7.56?

Write the word or phrase that best completes each statement or answers the question. Provide the missing information. -If f is defined on the interval [ $\left[ x _ { 1 } , x _ { 2 } \right]$ ], then the average rate of change of f on the interval [ $\left[ x _ { 1 } , x _ { 2 } \right]$ is given by the formula .

Solve the problem. - $\text { Use the graph of } y = b ( x ) \text { below to graph } y = b \left( \frac { 1 } { 2 } x \right) \text {. }$

Find the midpoint of the line segment whose endpoints are the given points. - $( 5.3,4.7 )$ and $( 7.2 , - 9.7 )$

Determine the slope and the y-intercept of the line. - $6 = - 6 y$

Write the word or phrase that best completes each statement or answers the question. Provide the missing information. - $\text { Given a point } \left( x _ { 1 } , y _ { 1 } \right) \text { on a line with slope } m \text {, the point-slope formula is given by ـــــــــــــــــــــ}$

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 -axis if replacing y by -y results in an equivalent equation.

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