Review Sheet for Test 2

Math 121 Review sheet for test 2

1. Find the profit function, which is a quadratic function, satisfies ALL the function
conditions:

a. the break even units for this profit function is at x = 50 and x = 150.
b. the maximum profit is $10, 000.

2. Find a polynomial f satisfies the following conditions:

a. f has repeated x − interecepts (even number of times ) at x= −1 and x = 3;
b. f has non-repeated x − intercepts at x = −2 and x = 4.
c. f(−5)< 0.

3. Sketch the graph which you have found in question above.

4. Find a polynomial f satisfies the following conditions:

a. f has repeated x − interecepts (even number of times ) at x = 3;
b. f has non-repeated x − intercepts at x = 1 and x = 4.
c.  f(5)< 0.

5. Sketch the graph which you have found in question above.

6. Find the profit function, which is a quadratic function and satisfies ALL the
following conditions: (a) the company breaks even when x = 100 and x = 300 units
are produced, (b) the maximum revenue is $40, 000.


(correct).
e. None of above.

7. Find a profit function P (x) satisfies the following conditions, where x denotes
number of units are produced and P (x) is a polynomial function: (a) the company
breaks even at x = 200,400 and 600 units (b) the profit function P (x) changes signs
(from P (x)> 0 to P (x)<0 or vise versa) at x = 400 but P (x) does not change sign
at x = 200 and 600, (c) the company is profitable when 50 units are produced.


(correct)

e. None of above.

8. For

a. find the x − intercepts of f,
b. find the interval(s) where f (x)> 0,
c. sketch the graph for f.

9. A company’s profit function P (x) (when x number of units are produced) resembles
a polynomial function and satisfies ALL the following conditions:

a. The profit function breaks even at x = 100,400 and 500 units.
b. The profit function P (x) changes signs (from P (x)> 0 to P (x)< 0 or vise versa)
at x = 100 but P (x) does not change signs at x = 400 and 500.
c. The company is profitable when 50 units are produced.
Then (a) find a profit function which satisfies all the conditions mentioned
above. (b) Predict if 300 units is produced, would the company be profitable?

10. True or False:

a. Any odd degree polynomial has at least one x -intercept.
b. Any even degree polynomial has at least one x -intercept.
c. The function has no x − intercept in the interval of [0, 1].
d. For a degree four polynomial, the number e will
affect the graphs of   in horizontal direction.

11. Find two functions which have the domain of and the range of

12. Let
a. Find the function f₁ so that the graph of   is being reflected along
x − axis.
b. Find the function f₂ so that the graph of   is being shifted to the right 2
units and down 3 units from f₁.