PRE CALCULUS Pre-Calculus Polynomial Functions 2

Question 1

Which of the following is a polynomial function?

Accepted Answer

f(x) = 2x³ - 5x + 7

Answer

A polynomial function has non-negative integer exponents only; 2x³ - 5x + 7 satisfies this.

Question 2

What is the end behavior of f(x) = -2x⁴ + 3x² - 1?

Accepted Answer

Down left, down right

Answer

Even degree with negative leading coefficient means both ends point downward.

Question 3

A polynomial of degree 5 can have at most how many turning points?

Accepted Answer

4

Answer

A degree-n polynomial has at most n - 1 turning points, so degree 5 gives at most 4.

Question 4

Which factor theorem statement is correct?

Accepted Answer

(x - c) is a factor if f(c) = 0

Answer

The Factor Theorem states (x - c) is a factor of f(x) if and only if f(c) = 0.

Question 5

If f(x) = x³ - 6x² + 11x - 6, what is f(1)?

Accepted Answer

0

Answer

f(1) = 1 - 6 + 11 - 6 = 0, so (x - 1) is a factor.

PRE CALCULUS Practice Test