# Identify the type of graphs and its domain and range

1) a) Given the above graph, identify the graph of the function (line, parabola, hyperbola, or exponential), explain your choice, and give the domain and range as shown in the graph, and also the domain and range of the entire function.

Graph Type:

Explantation:

Domain:

Range:

b) Given the above graph, identify the graph of the function (line, parabola, hyperbola, or exponential), explain your choice, and give the domain and range as shown in the graph, and also the domain and range of the entire function.

Graph Type:

Explantation:

Domain:

Range:

c) Given the graph above, identify the graph of the function (line, parabola, hyperbola, or exponential) and explain your choice.

Graph Type:

Explanation:

What happens to y as x gets larger?

What happens to x as y gets larger?

d) Given a line containing the points (1,4), (2,7), and (3,10) determine the slope-intercept form of the equation, provide one additional point on this line, and graph the function.

Equation in Slope-Intercept Form:

Give one additional point in (x,y) form that would fall on this line:

2) In most businesses, increasing prices of products can negatively impact the number of customers. A bus company in a small town has an average number of riders of 800 per day. The bus company charges $2.25 for a ride. They conducted a survey of their customers and found that they will lose approximately 40 customers per day for each $.25 increase in fare.

a) Let the number of riders be a function of the fare charged. Graph the function, identify the graph of the function (line, parabola, hyperbola, or exponential), find the slope of the graph, find the price at which there will be no more riders, and the maximum number of riders possible.

Graph:

Graph Type:

What is the slope of the graph?

b) The bus company has determined that even if they set the price very low, there is a maximum number of riders permitted each day. If the price is $0 (free), how many riders are permitted each day?

c) If the bus company sets the price too high, no one will be willing to ride the bus. Beginning at what ticket price will no one be willing to ride the bus?

3) It is approximately 480 miles from Los Angeles, California, to San Francisco, California. Allowing for various traffic conditions, a driver can average approximately 60 miles per hour.

a) How far have you traveled after 3 hours?

b) How far have you traveled after 4 hours?

c) How far have you traveled after t hours (i.e., write a linear function that expresses the distance traveled, d, as a function of time, t).

d) How far will you HAVE LEFT to travel to reach San Francisco after you have traveled 3 hours?

e) How far will you HAVE LEFT to travel to reach San Francisco after you have traveled 4 hours?

f) How far will you HAVE LEFT to travel to reach San Francisco after you have traveled t hours (i.e., write a linear function that expresses the distance to be traveled to reach San Francisco, s, as a function of time, t).

See attached file for full problem description.

## Solution This solution is **FREE** courtesy of BrainMass!

Please see the graphs and detailed solutions in the attached file.

2)

a) What is the slope of the graph?

It loses approximately 40 customers per day for each $.25 increase in fare, so the rate of change is the slope of the line:

-40/0.25=-160

Equation of line now is: y = -160x + b

A bus company in a small town has an average number of riders of y = 800 per day. The bus company charges x= $2.25 for a ride. S0 (2.25,800) is a point on the line

800 = -160*2.25 +b

b = 1160

The equation of line: y = -160x+1160

b) When the ride is free, we have y = -160 * 0 + 1160 = 1160

Hence the maximum number of riders per day is 1160.

c) It means y =0 when there is no more riders, so

0 = -160x + 1160

x = 1160 / 160 = 7.25

So when the price is $7.25, there will be no more riders.

3)

a) The distance traveled is d = vt

The speed is v = 60 mi/h , after t = 3 hours, d = vt = (60 mi/h) * (3h) = 180 miles.

b) after t = 4 hours, d = vt = (60 mi/h) * (4h) = 240 miles.

c) Distance = 60t, where 0 ≤ t ≤ 8

d) From (a) we know you have traveled 180 miles after 3 hours, and the total distance between the two cities is 480 miles. So the distance left is 480 - 180 = 300 miles.

e) From (b) we know you have traveled 240 miles after 4 hours, and the total distance between the two cities is 480 miles. So the distance left is 480 - 240 = 240 miles.

f) From (c) we know you have traveled 60t miles after t hours, and the total distance between the two cities is 480 miles. So the distance left is (480 - 60t) miles.