PRE CALCULUS Pre-Calculus Polynomial Functions 2 — Questions and Answers
Question 1: Which of the following is a polynomial function?
- f(x) = 3x² + √x - 1
- f(x) = 2x³ - 5x + 7 (Correct answer)
- f(x) = x⁻² + 4x
- f(x) = (x+1)/x
Correct answer: f(x) = 2x³ - 5x + 7
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?
- Up left, up right
- Down left, down right (Correct answer)
- Up left, down right
- Down left, up right
Correct answer: Down left, down right
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?
- 5
- 4 (Correct answer)
- 6
- 3
Correct answer: 4
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?
- (x - c) is a factor if f(c) ≠ 0
- (x - c) is a factor if f(c) = 0 (Correct answer)
- (x + c) is a factor if f(c) = 0
- (x - c) is a factor only when c > 0
Correct answer: (x - c) is a factor if f(c) = 0
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)?
- 0 (Correct answer)
- 1
- -1
- 6
Correct answer: 0
f(1) = 1 - 6 + 11 - 6 = 0, so (x - 1) is a factor.
Question 6: The multiplicity of a zero determines which graph behavior?
- The y-intercept location
- Whether the graph crosses or touches the x-axis at that zero (Correct answer)
- The number of complex roots
- The value of the leading coefficient
Correct answer: Whether the graph crosses or touches the x-axis at that zero
Odd multiplicity means the graph crosses the x-axis; even multiplicity means it touches and turns back.
Question 7: What is the y-intercept of f(x) = 4x³ - 2x² + x - 8?
- 4
- -2
- 1
- -8 (Correct answer)
Correct answer: -8
The y-intercept is f(0) = -8.
PRE CALCULUS Pre-Calculus Polynomial Functions 2
Which of the following is a polynomial function?