Exam 2: Functions and Graphs

Use Graphs to Locate Relative Maxima or Minima The graph of a function f is given. Use the graph to answer the question. -Find the numbers, if any, at which f has a relative maximum. What are the relative maxima?

The graph below shows the percentage of students enrolled in the College of Engineering at State University. Use the graph to answer the question. $\text { Percent of Students in College of Engineering }$ -If f represents the function, find f(1980).

Begin by graphing the standard square root function f(x) $f ( x ) = \sqrt { x }$ . Then use transformations of this graph to graph the given function. - $g ( x ) = - \sqrt { x + 2 } + 2$

Determine whether the equation defines y as a function of x. - $y ^ { 2 } = 3 x$

Identify the intervals where the function is changing as requested. -Constant

Find the distance between the pair of points. - $( - 3 , - 1 )$ and $( 1 , - 3 )$

Use the graph of f to draw the graph of its inverse function. -

Determine whether the given function is even, odd, or neither. -

Use the given conditions to write an equation for the line in slope-intercept form. -Slope $= \frac { 2 } { 3 }$ , passing through $( 8,5 )$

Determine whether the equation defines y as a function of x. - $x + y ^ { 3 } = 1$

Begin by graphing the standard square root function f(x) $f ( x ) = \sqrt { x }$ . Then use transformations of this graph to graph the given function. - $g ( x ) = \sqrt { - x - 5 }$

Does the graph represent a function that has an inverse function? -

Find the slope of the line that goes through the given points.. - $\left( \frac { 1 } { 2 } , 2 \right)$ and $\left( \frac { 1 } { 2 } , - 4 \right)$

Solve. -When making a telephone call using a calling card, a call lasting 6 minutes cost $\$ 2.90$ . A call lasting 15 minutes cost $\$ 6.50$ . Let $y$ be the cost of making a call lasting $x$ minutes using a calling card. Write a linear equation that models the cost of a making a call lasting $x$ minutes.

Solve. -When making a telephone call using a calling card, a call lasting 5 minutes cost $\$ 0.90$ . A call lasting 12 minutes cost $\$ 1.60$ . Let $y$ be the cost of making a call lasting $x$ minutes using a calling card. Write a linear equation that models the cost of making a call lasting $x$ minutes.

Graph the linear function by plotting the x- and y-intercepts. - $50 x-30 y-150=0$

Find the inverse of the one-to-one function. - $f ( x ) = \sqrt [ 3 ] { x - 5 }$

Complete the square and write the equation in standard form. Then give the center and radius of the circle. - $x ^ { 2 } + y ^ { 2 } + 4 x + 8 y + 16 = 0$

Given functions f and g, perform the indicated operations. - $f ( x ) = 4 x + 5 , \quad g ( x ) = 3 x + 3$

Find the domain of the function. - $f ( x ) = \frac { x } { x ^ { 2 } + 19 }$