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# 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.

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