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# Discussing Functions and Linear Equations

Hi, I need some assistance computing the following mathematical questions so that I can create a study guide.

1. What is a function?

2. What is a linear function?

3. What form does a linear function take? (e.e., What is the standard mathematical notation of a linear function?)

4. What is the formula for determining the slope of a line?

5. Suppose you have a lemonade stand, and when you charge \$1 per cup of lemonade you sell 60 cups. But when you raise your price to \$1.50 you only sell 30 cups. Write an equation for the number of cups you sell as a function of the price you charge. Denote "C" for the number of cups, and "P" for the price you charge. Assume the function is linear.

6. Take a look at the table below and compute an equation for f(x).

x -3 -2 1 3 4
_________________

F(x) 0 3 12 18 21

7. Which of the following are functions? Explain your reasoning for a, b, and c. Keep the definition of a function strongly in mind as you do this problem, it is not nearly as difficult as it may look. Think about whether the relationship between f(x) and x is consistent with being a function or not and explain your reasoning. Problems b & c are multi part relations so consider all parts when determining if they are functions.

a. f(x) = x^8

b. f(x) = 45 if x>2 otherwise f(x) = -4

c. f(x) = 4 if x>0 or f(x) = -4 if x<0 or f(x) = 4 or -4 if x = 0

8. For each of the relationships below, explain whether you think it is best described by a linear function or a non-linear function. Explain your reasoning thoroughly.

a. The time it takes you to get to work as a function the speed at which you drive.

b. The probability of getting into a car accident as a function of the speed at which you drive.

c. A person's height as a function of the person's age (from age 0 to 100).

#### Solution Preview

1. What is a function?
A function is a relationship between two sets of numbers where every element from the first set (the domain) is assigned another value from the second set (the range). Every element in the domain can only be assigned to one value in the range, while a element in the range may be assigned many values from the domain.

2. What is a linear function?
A linear function is a function where the domain and the range change in equal proportion. For example, if x increases from 2 to 3 (1 unit) and y increases by 6 units, then if x increases from 7 to 8, y would also increase by 6 units.

3. What form does a linear function take?
Y = mx + b

4. What is the formula for determining the slope of a line?
Slope = change in y/change in x = (y1 ...

#### Solution Summary

In about 630 words, this solution discusses an array of mathematical based questions all related to the concept of functions and working with linear functions in particular. Explanations and the proper calculations are provided for each question.

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