Graphing and Word Problems
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IP Unit 1
1)
a)
Given the above graph, identify the graph of the function (line, parabola, hyperbola, or exponential), and give the domain and range as shown in the graph.
Graph Type
Explanation of why you chose that graph type:
Domain
Range
b)
Given the above graph, identify the graph of the function (line, parabola, hyperbola, or exponential), explain in your works, and why you chose that graph type.
Graph Type
Explanation of why you chose that graph type:
Domain
Range
c)
Notice the impact of y being undefined at x = 0. The graph gets infinitely close to the y axis (where x=0) but never touches it since y is undefined for an x of 0.
Given the graph above, identify the graph of the function (line, parabola, hyperbola, or exponential), and explain, in your own words, why you chose that graph type.
Graph Type
Explanation of why you chose that graph type:
What happens to y as x gets larger?
What happens to x as y gets larger?
d) Given a line containing the points (1,3), (2,4), (3,5) determine the slope-intercept form of the equation, give one additional point on this line and graph the function.
Equation of line in slope-intercept form
Show your work here:
Give one additional point in (x,y) form that would fall on this line:
Graph the function:
2) In most businesses, increasing prices of their product can have a negative effect on the number of customers of the business. A bus company in a small town has an average number of riders of 1,000 per day. The bus company charges $2.00 for a ride. They conducted a survey of their customers and found that they will lose approximately 50 customers per day for each $.25 increase in fare.
a) Given the description above, 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 find the maximum number of riders possible. The vertical axis is the number of riders per day, and the horizontal axis is the fare.
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?
Answer:
Show work in this space:
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?
Answer:
Show work in this space:
3) It is approximately 300 miles from Chicago, Illinois, to St. Louis, Missouri. Allowing for various traffic conditions, a driver can average approximately 60 miles per hour.
a) How far have you traveled after 3 hours?
Answer:
Show work in this space:
b) How far have you traveled after 4 hours?
Answer:
Show work in this space:
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.
Answer:
d) How far will you HAVE LEFT to travel to reach St. Louis after you have traveled 3 hours?
Answer:
Show work in this space:
e) How far will you HAVE LEFT to travel to reach St. Louis after you have traveled 4 hours?
Answer:
Show work in this space:
f) How far will you HAVE LEFT to travel to reach St. Louis after you have traveled t hours? i.e. write a linear function that expresses the distance to be traveled to reach St. Louis, s, as a function of time, t.
Answer:
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Solution Summary
Graphing problems are solved.
Education
- BSc , Wuhan Univ. China
- MA, Shandong Univ.
Recent Feedback
- "Your solution, looks excellent. I recognize things from previous chapters. I have seen the standard deviation formula you used to get 5.154. I do understand the Central Limit Theorem needs the sample size (n) to be greater than 30, we have 100. I do understand the sample mean(s) of the population will follow a normal distribution, and that CLT states the sample mean of population is the population (mean), we have 143.74. But when and WHY do we use the standard deviation formula where you got 5.154. WHEN & Why use standard deviation of the sample mean. I don't understand, why don't we simply use the "100" I understand that standard deviation is the square root of variance. I do understand that the variance is the square of the differences of each sample data value minus the mean. But somehow, why not use 100, why use standard deviation of sample mean? Please help explain."
- "excellent work"
- "Thank you so much for all of your help!!! I will be posting another assignment. Please let me know (once posted), if the credits I'm offering is enough or you ! Thanks again!"
- "Thank you"
- "Thank you very much for your valuable time and assistance!"
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