I need answers please help

Question

1.  Inspired by her new love of math developed in Bridge to College Math, Susan decides to open a math tutoring center. She found a nice office that she can lease for $400 per month. Susan is going to charge $25 per hour for her tutoring service. She is examining her monthly budget.

 

1. Write an equation using function notation to model Susan’s monthly income as a function of the number of hours (x) she spends tutoring in one month.
2. What is the slope of the function and what does it mean in the context of this problem?
3. What is the x-intercept and what does it mean in the context of this problem?
4. What is the y-intercept and what does it mean in the context of this problem?
5. What is the domain of the function in the context of this problem, and why?
6. What is the range of the function in the context of this problem, and why?
7. Graph the function. Label the scale and axes.

Answer 1

Monthly Income = f(x) = 25x -400

slope=25 =$25 = hourly wage

y intercept = -400 = -$400 = monthly cost

domain is: 0 < x < about the number of waking hours in a month = 8x30 = 240

which = available working hours

range is: -400 < y < 240(25)-400 = $5,600 = maximum amount she can make in a month, minimum she makes is a loss of $400.

The graph is a fairly steep upward sloping straight line with slope = 25 and y intercept = -400