Exam 1: Functions, Graphs, and Models; Linear Functions

Suppose the cost of producing x objects was defined by the function $C ( x ) = \frac { 60 x } { \sqrt { 60 x - 10 } }$ What is the domain of the function defined by this equation?

Evaluate the function. -Given $f ( x ) = 19 x - 4$ , find $f ( 17 )$ .

Is it possible for the x-intercept and the y-intercept of a straight line to be at the same point? Explain your answer.

Crafty Bill's Cool Car Sales opened as a used car sales lot in 2006. The graph shows the number of cars sold f as a function of time t. Find and interpret f(2010).

Write the equation of the line using the information given about its graph. -Slope $- \frac { 2 } { 9 } , \mathrm { y }$ -intercept 3

State whether the graph is or is not that of a function. -

State whether the graph is or is not that of a function. -

Decide whether or not the set of ordered pairs defines a function. - $\{ ( 1,4 ) , ( 2,5 ) , ( 5 , - 3 ) , ( 7,5 ) , ( 11,8 ) \}$

Write the equation of the line whose graph is shown. -

Use a graphing utility to graph the function and then answer the question. -The number of mosquitoes $\mathrm { M } ( \mathrm { x } )$ , in millions, in a certain area depends on the June rainfall $x$ , in inches: $M ( x ) = 4 x - x ^ { 2 }$ . What rainfall produces the maximum number of mosquitoes?

The percent p of high school students who participate in sports at a public high school can be modeled by 10 p $16 x = 224$ , where $x$ is the number of years after 2010 . Interpret the slope as a rate of change if $x$ is the independent variable.

Graph the equation. - $4 x=y+2$

The following graph shows the stock price of a new internet company over the first 18 months after the initial public offering of its stock. Approximately in which month(s) did the stock price reach $70?

Determine if there is a linear relationship between the variables in the table. Height (inches) 57 60 72 59 63 65 66 68 61 Time (seconds) 32.9 40.1 35.7 41.8 47.4 37.3 39.1 41.5 32.8

Determine whether the given relationship defines a function. If so, identify the independent and dependent variable, and why the relationship is a function. -The balance in a checking account b at the close of business on a given day x.

Decide whether or not the set of ordered pairs defines a function. - $\{ ( - 8 , - 8 ) , ( - 3,8 ) , ( - 2 , - 8 ) , ( 2 , - 5 ) \}$

Provide an appropriate response. -Explain the process used to find the equation of a line through two different points.

The forearm length in centimeters, A, can be approximated by a linear function of the foot length in centimeters, f. Use the points (25, 24) and (33, 33) to find a linear model for the data in the table below. Foot Length () 29 31 33 26 28 37 25 30 32 Forearm Length () 30 30 33 25 28 37 24 31 31

Determine a viewing window that will provide a complete graph of the function. - $y = 0.62 x ^ { 3 } - 5 x ^ { 2 } + 11 x + 8$

Write the equation of the line whose graph is shown. -