## Math for Social Sciences. Practice Exam

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

Answer: The slope is .

• graph: • y-intercept:

Answer: The y-intercept is (0,4).

• x-intercept:

Answer: The x-intercept is (3,0).

• • slope:

Answer: The slope is 0.

• graph: • y-intercept:

Answer: The y-intercept is (0,-5).

• x-intercept:

Answer: There is no x-intercept.

2. Answer the following:
• Find the slope of the line perpendicular to .

Answer: The slope of the line perpendicular is -2.

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

Answer: An equation for the line is y+1=-2(x-3).

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).

Answer: The revenue function is R(x)=150x.

• Find the profit function, P(x).

Answer: The profit function is .

• What is the maximum profit, and how many units must be produced in order to realize this profit?

Answer: The maximum profit is \$625, at a production level of 75 units.

• What is the average cost per unit to produce 10 units?

Answer: The average cost is \$510 per unit.

• What is the average cost per unit to produce 50 units?

Answer: The average cost is \$150 per unit.

5. Which of the following (if any) represent y as a function of x?
• a) Answer: This is not a function.

• b) .

Answer: This is not a function.

• c) 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.

• For 5a, there are two different values in the range (5, and 4) for the same value in the domain ( 3 ). This does not fulfill the definition of a function.
• For 5b: For many values of x (the domain) there will be two values for y (the range). For example, x=4 corresponds to both y=1 and y=-1.
6. Evaluate the following for the function: • Domain.

Answer: The domain is .

• f(0).

Answer: .

• f(m+3).

Answer: .

7. Let Note: (When multiplied out, )
• Does the graph open up or down?

Answer: The graph opens up.

• What feature of the function, did you use to answer part(a)?

Answer: The leading coefficient (in front of the term) determines if the function opens up or opens down. If the coefficient is positive, then the graph opens up. If the coefficient is negative, then the graph opens down.

• What are the coordinates of the vertex?

Answer: The coordinates of the vertex are (-2,-1).

• Find the y-intercept.

Answer: The y-intercept is (0,3).

• Find the x-intercept(s).

Answer: The x-intercepts are (-1,0), and (-3,0).

• Sketch the graph showing (a) - (e).