Exam 2: Functions and Relations

Write the word or phrase that best completes each statement or answers the question. Provide the missing information. -Given a function defined by y = f (x), the statement f (2) = 4 is equivalent to what ordered pair?

Find the indicated function and write its domain in interval notation. - $s ( x ) = \frac { x - 2 } { x ^ { 2 } - 9 } , t ( x ) = \frac { x - 3 } { 2 - x } , ( s + t ) ( x ) = ?$

Solve the problem. - $f ( x ) = \{ ( - 6,6 ) , ( - 2 , - 3 ) , ( 5 , - 8 ) , ( 1,9 ) \} , g ( x ) = ( 2,5 ) , ( 1,8 ) , ( 9 , - 6 ) , ( - 2 , - 3 ) \}$ Find $( f \circ g ) ( 1 )$

Use the given information about a circle to write an equation of the circle in standard form. -The endpoints of a diameter are $( 3,11 )$ and $( - 9 , - 5 )$ .

Write the domain in interval notation. - $f ( x ) = \frac { 4 } { \sqrt { 3 - x } }$

Evaluate as indicated. -If $K ( x ) = | x - 9 | + x$ , find $K ( - 7 )$ .

Use transformations on the basic functions to write a rule y = f (x) that would produce the given graph. -

The graph of y = f (x) is given. Graph the indicated function. -Graph $y = 2 f ( x + 1 ) + 4$

The midpoint of the line segment with endpoints ( $\left( x _ { 1 } , y _ { 1 } \right) \text { and } \left( x _ { 2 } , y _ { 2 } \right)$ ) is given by the formula .

A y-intercept of a graph has an x-coordinate of________ .

Solve the problem. -A chess master creates instructional videos about various opening strategies. She sells the videos in 3 -hr packages for $\$ 35$ each. Her one-time initial cost to produce each 3 -hr video package is $\$ 4,600$ (this includes labor and the cost of computer supplies). The cost to package and ship each DVD is \$2.95. a. Write a linear cost function that represents the cost $C ( x )$ to produce, package, and ship $x 3 - \mathrm { hr }$ video packages. b. Write a linear revenue function to represent the revenue $R ( x )$ for selling $x 3$ -hr video packages. c. Evaluate $( R - C ) ( x )$ and interpret its meaning in the context of this problem.

Write the word or phrase that best completes each statement or answers the question. Provide the missing information. -An equation of the form x = k where k is a constant represents the graph of a line.

Identify the set of values x for which y will be a real number. - $y = \frac { 10 } { x + 7 }$

Solve the problem. -The figure represents the average credit card debt for selected households in Silerville. $\text { Average Credit Card Debt, Selected Households }$ Let y represent the credit card debt in dollars. Let x represent the year, where x = 0 corresponds to the year 1990, x = 4 represents 1994, and so on. a. Use the ordered pairs given in the graph, (0, 3844) and (16, 8304) to find a linear equation to estimate the Average credit card debt versus the year. Round the slope to the nearest tenth. b. Use the model from (a) to estimate the average debt in 1,997. Round to the nearest dollar.

Write the given equation in the form $( x - h ) ^ { 2 } + ( y - k ) ^ { 2 } = r ^ { 2 }$ . Identify the center and radius. - $x ^ { 2 } + y ^ { 2 } + 8 x - 10 y + 25 = 0$

Determine the x- and y-intercepts for the given function. - $q ( x ) = - x ^ { 2 } + 18$

Write the domain in interval notation. - $w ( a ) = \frac { 4 } { 6 - | a - 3 | }$

Identify the location and value of any relative maxima or minima of the function. -

Identify the location and value of any relative maxima or minima of the function. -

Write an equation of the line satisfying the given conditions. -The line passes through (25, 24) and is perpendicular to y = 6.