# 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 f_{1} so that the graph of
is being reflected along

x − axis.

b. Find the function f_{2} so that the graph of
is being shifted to the
right 2

units and down 3 units from f_{1}.

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