Directions: Read carefully. You should be able to solve these questions without your graphing calculator. Choose the best answers.

 1. Given: f (x) = (2x + 1)(x + 3)(x - 2) For what values of x is f (x) > 0 ? (Check all that apply, and hit SUBMIT!) x < -3 -3 < x < -½ -3 < x < 2 -½ < x < 2 x > -½ x > 2

2.
Regarding the graph at the right, the function is:

Choose:
 odd. increasing on interval (-∞,-3). positive on interval (3,∞). symmetric about the origin.

3.
Given: f (x) = (2x + 1)(x + 3)(x - 2)
How many relative maxima does this function have?

Choose:
 one two three none

 4. A fifth degree polynomial function is shown below. Which of the statements are NOT true about this function? (Check all that apply, and hit SUBMIT!) leading coefficient is positive function is odd only two relative maximums only two intervals of decreasing positive from x = -2 to x = 1.75 exactly 5 zeroes as x → ∞, y → ∞

5.
Given h(x) = -(x - 1)(x + 2)(x - 5)
What are the end behaviors of the graph of this function?

Choose:

6.
Which of the following polynomial functions could be represented by the graph at the right?

Choose:
 f (x) = x3 + 4x2 + x - 1 f (x) = x3 + 3x2 + x + 1 f (x) = x3 + 4x2 + x + 1 f (x) = x3 + 3x2 + x - 1

 7. Which of the statements are true about these functions? (Check all that apply, and hit SUBMIT!) the graph of g(x) opens downward function g(x) is even in f (x), as x → ∞, y → ∞ f (x) and g(x) share a zero f (x) is negative on interval (-2,3) g(x) is positive on interval (-2,0) in g(x), as x → -∞, y → ∞

8.
Which of the following functions represents a polynomial function with degree 3, roots x = 0, x = -1 and x = 2, and with end behavior approaching positive infinity as x approaches negative infinity?

Choose:
 g (x) = x(x + 1)(x - 2) g (x) = x(x - 1)(x + 2) g (x) = -x(x + 1)(x - 2) g (x) = -x(x - 1)(x + 2)

9.
Given: f (x) = (x + 1)2(3 - x)
Which of the following statements is FALSE regarding its graph?

Choose:
 As x → ∞, f (x) → -∞. There is one relative maximum point. There is one relative minimum point. As x → -∞, f (x) → -∞.

10.
Given: f (x) = x2 - 16
On which interval(s) is this function positive?

Choose:
 (- ∞, 0) (0, ∞) (-16, ∞) (-∞, -4) and (4, ∞)