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1. Which of the following are functions? Explain your reasoning for a, b, and c.

a. f(x)=1 if x>1
f(x)=0 otherwise

b. f(x)=2 if x>0
f(x)=-2 if x<0
f(x)=2 or -2 if x=0

c. f(x)=5/x

2. 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 $2 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 number of cups, and "P" for the price you charge. Assume the function is linear.

3. Take a look at the table below and write out an equation for f(x).
x -2 -1 0 1 2
f(x)-1 1 3 5 7

4. 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 throughly.

a. How fast it takes you to get to work as a function of how fast you drive.

b. Probability of getting into a car accident as a function of how fast you drive.

c. Your height as a function of age (from age 0 to 100)

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Please answer question below in attachment.

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The lowest and highest data points in a set of data are (1 year, $77) and (6 years, $ 67). Demonstrate how to use the High-Low Method to find the equation of the line that fits this data. (Hint: The High-Low method of fitting a line through a collection of linear data(data points) is to draw a straight line through the first(lowest) and last(highest) data point. With the 2 data points, you can find out the slope of the line. Then apply “Point-Slope Form” to generate an equation for the line. The idea of using coordinates of 2 data point to find the slope and using point-slope form to generate a line( slope formula, example 1: point slope form, example 2) The line can go from High-Low or Low-High.

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1) -12=-x-4y (solve for y when x =3, y=?
2) 2x+5y=10, solve for y when x=-7,7=?
3) give the solution set for y+7/8<1/2

give the slope and y-intercept of the following graphs.
4) x+y=4
5) 5x+3y=15
6) 20x - 240 = -60y
7) 10x-300=-40y
8) 3x=4y-12

write the equation of the line in the slope-intercept form:
9) y+2+-5(x+4)
10) x intercept = 4 and y-intercept=-2

Answer the following

11) find the area and circumference of a circle whose diameter measures 12 centimeters

12) Find the area of a cylinder whose radius is 2 inches and whose height is three inches

13) the maintenance bill for a shopping center containing 180,000 square fee is $45,000. What is the bill for a store in the center that is 4,800 square feet?

14) A new car costs 125% of what it cost 4 years ago. Determine the price 4 years ago if the car now sells for $32,500.

Problem text:

is an algebra problem here it is:

5.4*10^-6C/x^2=2.2*10^-6C/(1.00m-x)^2 solve for x
the answer is x=.61 meters..how do I get to this answer?

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Use the Graph of f(x)=x^2 to sketch the graph of the function by hand. verify with a graphing utility.

g(x)=(x+1)^2-3

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Q Find (a)f g and (b)g f

f(x)=2x-3, g(x)=2x-3

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Q. Determine the domain of (a) f, (b)g, and (c)f g

f(x)=2x+3, g(x)=x/2

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Q. Determine whether the function has an inverse function. If it does, find its inverse function

f(x)=36+x^2, x<=0

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Q. Sketch the graph of the Quadratic function. Identifythe vertex and intercepts

f(x)=-(x^2+6x-3)