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

Write the equation of the line using the information given about its graph. -Slope $- \frac { 3 } { 4 } , \mathrm { y }$ -intercept $\frac { 11 } { 4 }$

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

It costs $34 per hour plus a flat fee of $17 for a plumber to make a house call. Find the total cost to have a plumber come to a house for 6 hours.

The table below shows the weight for a calf raised by a local rancher. Use the information to determine the average rate of change in the calf's weight per day. Calf's Weight Day Weight (in lbs) 1 505 5 525 15 575 25 625 40 700

Suppose the monthly cost for manufacturing bar stools i $C ( x ) = 529 + 23 x$ x, where x is the number of bar stools produced each month. Find and interpret the marginal cost for the product.

Decide whether or not the equation defines y as a function of x. - $y = \frac { 6 } { x + 19 }$

Graph the function with a graphing utility. - $y = - x ^ { 2 } + 2 x - 5$

Determine whether or not the relationship shown in the table is a function. - Name Test Score Bob L. 80 Susan H. 83 Jim H. 76 Bruce B. 96 Does the table define test score as a function of name?

Find the domain of the function. - $y = \sqrt { 6 x - 5 }$

The polynomial $0.0032 x ^ { 3 } - 0.0058 x ^ { 2 } + 0.131 x + 1.41$ gives the approximate total earnings of a company, in millions of dollars, where $x = 0$ corresponds to $2008 , x = 1$ corresponds to 2009 , and so on. This model is valid for the years from 2008 to 2012 . Determine the earnings for 2012. Round your answer to the nearest hundredth million.

Provide an appropriate response. - $\text { The equation } ـــ = - 7 \text { has a horizontal line as its graph. }$

Determine whether the given relationship defines a function. If so, identify the independent and dependent variable, and why the relationship is a function. -The temperature t on a backyard thermometer on a given day x.

$4 y=-24+6 x$

A boat is moving away from shore in such a way that at time thours its distance from shore, in kilometers, is given by the linear function d(t)=4.5t+9.1 . What is the rate of change of the distance from shore?

Determine if the graph represents a function. -

Find the domain of the function. - $y = \frac { 17 } { 12 - x }$

Provide an appropriate response. -Consider the linear function f(x) $f ( x ) = 5 x + 20$ 20. What is the domain and range of this function? Now, suppose the function represents the relationship between studying time and grades on an exam. The variable x represents the number of hours spent studying and f(x) represents the grade on the exam. Does this change the domain and range? If so, what is the new domain and range and why is it different?

Find the domain of the function. - $y = 6 - \frac { 1 } { x }$

Why is the slope of a horizontal line equal to zero? Give an example.

A deep sea diving bell is being lowered at a constant rate. After 12 minutes, the bell is at a depth of 400 ft. After 45 minutes the bell is at a depth of 1700 ft. What is the average rate of lowering per minute?