## Math for Social Sciences. Practice Exam

1. For each of the linear equations below, find the following (if they exist):
• slope:
• graph:
• y-intercept:
• x-intercept:

• slope:
• graph:
• y-intercept:
• x-intercept:

• Find the slope of the line perpendicular to .
• Find an equation for the line which passes through the point (3,-1) and which is perpendicular to the line . ( Hint: Use part(a)).

3. Sketch the graph of

showing the intercepts.

4. The cost of producing x units of a product is given by:

where C(x) is in dollars. The product sells for \$150 per unit.

• Find the revenue function, R(x).
• Find the profit function, P(x).
• What is the maximum profit, and how many units must be produced in order to realize this profit?
• What is the average cost per unit to produce 10 units?
• What is the average cost per unit to produce 50 units?

5. Which of the following (if any) represent y as a function of x?
• .
• Explain your answers to 5a, and 5b. That is, if you believe that 5a is (or is not) a function, explain how you came to this conclusion. Do the same for 5b.

6. Evaluate the following for the function:
• Domain.
• f(0).
• f(m+3).

7. Let Note: (When multiplied out, )
• Does the graph open up or down?
• What feature of the function, did you use to answer part(a)?
• What are the coordinates of the vertex?
• Find the y-intercept.
• Find the x-intercept(s).
• Sketch the graph showing (a) - (e).