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Math 1111 Practice Tests #2

SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.

Answer the question.

1) If the vertex of the graph of a quadratic function lies in quadrant IV and the graph opens
up, how many x-intercepts does the graph have?

 

MULTIPLE CHOICE . Choose the one alternative that best completes the statement or answers the question.

Evaluate the discriminant, and predict the type and number of solutions .

A) 3, two different irrational
B) 3, two different rational
C) 0, one rational
D) -3, two different imaginary

Solve the inequality analytically. Support the answer graphically. Give exact values for endpoints .

SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.

Provide an appropriate response.

4) Sketch the graph of a quadratic function for which the value of the discriminant is
positive, the vertex lies in quadrant IV, and the graph opens upward.

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.

5) Fill in the blanks to complete the statement.

The equation g(x) = 0 has ____ real solution(s). The value of the discriminant of g(x) is ____ .

A) 1; positive
B) 2; 0
C) 0; negative
D) 1; 0

6) Fill in the blanks to complete the statement.

The equation f(x) = 0 has ____ real solution(s) and ____ imaginary solution(s).

A) 1; 1
B) 2; 0
C) 0; 2
D) 0; 0

Find the correct end behavior diagram for the given polynomial function .

Find the equation that the given graph represents.

SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.

Provide the appropriate response.

10) Sketch the graph of a polynomial function which has a negative y -intercept, one local
maximum and one local minimum, but has no absolute extrema.

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.

11) Fill in the blanks with the words "odd" and "even". A polynomial function of ___ degree must have
at least one real zero, but a polynomial of ___ degree may have no real zeros . The range of a
polynomial function of ___ degree is (-∞, ∞).

A) odd; even; odd
B) even; odd; odd
C) odd; even; even
D) even; odd; even

Solve the polynomial inequality by graphing .

Provide the appropriate response.

13) Suppose that the complete graph of a cubic function shows that -6, 5, and 6 are the x-intercepts,
and the end behavior is described by f(x) → ∞ as x → -∞ and f(x) → -∞ as x → ∞. Find the solution
set of f(x) < 0.

A) (-∞, -6) ∪ (6, ∞)
B)(-∞, -6) ∪ (5, 6)
C) (-6, 6)
D) (-6, 5) ∪ (6, ∞)

SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question

Solve the equation for all complex solutions , giving exact forms in your solution set .

Write the solutions in interval notation below

f(x) = 0 __________________________________________
f(x) < 0 __________________________________________
f(x) > 0 __________________________________________

16) Solve the inequality x^3 — 9x < 0.
Write your solution in interval notation
__________________________________________
Graph on the number line
____________________________________________________________

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.

Solve the problem.

17) A farmer has 1400 feet of fence with which to fence a rectangular plot of land. The plot lies along a
river so that only three sides need to be fenced. Estimate the largest area that can be fenced.

Write the function f(x) that models the area of the fence.

SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.

18) Based on what we have learned about polynomial functions, write the factored form of this
function

f(x) = _____________________________________________________

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