MA 109 College Algebra Name: Sec.: EXAM 3 - REVIEW 1. In the picture ...

MA 109 -- College Algebra EXAM 3 - REVIEW

Name:

Sec.:

1. In the picture below, the graph of y = f (x) is the solid graph, and the graph of y = g(x) is the dashed graph. Find a formula for g(x). y10

9

8

7

6

5

4

3

2

1

0

x -10 -9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10 -1

-2

Possibilities:

-3

-4

(a) g(x) = f (2x) -5

(b) g(x) = 2f (x)

-6

(c) g(x) = f

1 2

x

-7

-8

(d) g(x) = -2f (x)

-9

(e)

g(x) =

1 2

f

(x)

-10

2. Suppose that the graph of y = f (x) contains the point (5,3). Find a point on the graph of y = 2f (x) - 4.

3. Find the vertex of y = 4x2 - 40x + 102.

4. Suppose that the graph of y = f (x) contains the point (10,-20). Find a point on the graph of y = f (5x) + 7.

1

5. In the picture below, the graph of y = f (x) is the solid graph, and the graph of y = g(x) is the dashed graph. Find a formula for g(x). y10

9

8

7

6

5

4

3

2

1

0

x -10 -9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10 -1

-2

Possibilities:

-3

-4

(a) g(x) = 3f (x) -5

(b) g(x) = -3f (x)

-6

(c) g(x) = f (3x)

-7

-8

(d) g(x) = f

1 3

x

-9

(e)

g(x) =

1 3

f

(x)

-10

6. Circle the even functions. Put a box around the odd functions.

(a). a(x) = |x| (b). b(x) = |x| + 1 (c). c(x) = x3 (d). d(x) = x3 + 1 (e). e(x) = 5 (f). f (x) = x4 (g). g(x) = x4 + 1 (h). h(x) = (x + 1)4 (i). i(x) = (x + 1)3 (j). j(x) = |x + 1| (k). k(x) = x

(l). l(x) = x

(m). m(x) = 3 x (n). n(x) = 0

2

7. Find the vertex of y = -4x2 - 24x - 29.

8. Suppose that the graph of y = f (x) contains the point (10,-20). Find a point on the graph of y = f (5x) + 7.

9. Does the graph of y = 3x2 + 12x - 5 have a maximum or a minimum? What is it?

10. In the picture below, the graph of y = f (x) is the solid graph, and the graph of y = g(x) is the dashed graph. Find a formula for g(x) in terms of f (xy)1.0

9 8 7 6 5 4 3 2 1 0

x -10 -9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10 -1 -2 -3 -4 -5 -6 -7 -8 -9 -10

11. The graph of an even function is symmetric with respect to

.

12. The graph of an odd function is symmetric with respect to

.

13. Suppose that the graph of y = f (x) contains the point (-2,7). Find a point on the graph of y = 5f (x + 3).

14. Let P (x) = 4x2 + 3x + 35. Find the y-intercept of the graph of y = P (x).

3

15. Find a formula for the parabola with vertex (6, -1) and that passes through the point (7, -4).

16. Let f (x) = x2 + 1 and g(x) = 3x - 5. Find f (g(x)).

17. In the picture below, the graph of y = f (x) is the solid graph, and the graph of y = g(x) is the dashed graph. Use the graphs to evaluate f (g(2)).

y 5

4

3

2

1

0

-5

-4

-3

-2

-1

0

1

2

3

4

5

x

-1

-2

-3

-4

-5

18. If the GGMC corporation produces x kilograms of gadgets, then their revenue, in dollars, is given by R(x) = 100 + 900x - .2x2. What is the maximum revenue and how many kilograms of gadgets should be manufactures to obtain this maximum?

Maximum Revenue:

Kilograms of Gadgets:

19. Let P (x) = x3 - 3x - 2x2 + 6. Find the real zeros of P(x).

20. Let f (x) = x - 3 and g(x) = 4 - x. Find the domain of (f + g)(x).

4

21. Let f (x) = 3x - 7. Find f (f (x))

22. You wish to purchase a new cell phone. You have a coupon for $10 and the store is running a special which allows you to deduct 15% from the price. If the original price of the cell phone is 175 dollars, what is the final price if you apply the coupon and then apply the 15% discount.

23. You wish to purchase a new cell phone. You have a coupon for $10 and the store is running a special which allows you to deduct 15% from the price. If the original price of the cell phone is 175 dollars find the final price if you apply the 15% discount and then apply the coupon.

24. Let P (x) = 7x15 - 2x7 + 3x2 + 8. List all possible rational zeros of P (x) given by the Rational Zeros Theorem (but do not check to see which are actually zeros). Possibilities: (a) ?1, ?8, ?8/7 (b) ?1, ?2, ?4, ?8, ?1/7, ?2/7, ?4/7, ?8/7 (c) ?1, ?8, ?7/8 (d) ?1, ?2, ?4, ?8, ?7, ?7/2, ?7/4, ?7/8 (e) ?1, ?1/2, ?1/4, ?1/8, ?7, ?7/2, ?7/4, ?7/8

25. Which of the following functions are one-to-one? (a). a(x) = |x| (b). b(x) = x3 (c). c(x) = x3 + 1 (d). d(x) = 5 (e). e(x) = x4 (f). f (x) = x4 + 1 (g). g(x) = (x + 1)3 (h). h(x) = |x + 1| (i). i(x) = 2x + 3 (j). j(x) = x (k). k(x) = 3 x (l). l(x) = 0

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