Question 1

Which of the following is the general form of a polynomial function in one variable?

Accepted Answer

$$f(x) = a_n x^n + a_{n-1} x$$^{n-1}$$ + \ldots + a_1$ x + a_0$

Question 2

Given the polynomial $$f(x) = 6x^4$ - 3x^2$ + 5$$, what is the degree and the leading coefficient?

Accepted Answer

Degree: 4, Leading coefficient: 6

Question 3

Which of the following functions is NOT a polynomial function?

Accepted Answer

$$g(x) = \frac{1}{x}$$

Question 4

A linear function is represented by which of the following equations?

Accepted Answer

$$f(x) = mx + b$$

Question 5

Which graph best describes a quadratic function?

Accepted Answer

A parabola that opens up or down

Question 6

If $$f(x) = 0$$ for all $$x$$, what is the degree of the polynomial?

Accepted Answer

No degree (undefined)

Question 7

Which of the following is a constant function?

Accepted Answer

$$f(x) = 7$$

Question 8

Given $$g(x) = 5(x - 4)^2$, what is the degree of g(x$$)$$?

Accepted Answer

2

Question 9

Which of the following statements about polynomial functions is TRUE?

Accepted Answer

The domain of a polynomial function is all real numbers.

Question 10

A company models its profit with $$P(x) = 2x^2$ - 5x + 3$$, where $$x is $$the number of products sold. What type of function is $$P(x)$$?

Accepted Answer

Quadratic function

Question 11

Which of the following is the correct description of the graph of $$f(x) = ax^2$ + bx + c$$ when $$a \u003c 0$$?

Accepted Answer

Parabola opens downward

Question 12

If $$f(x) = 2x - 1$$, which of the following best describes its graph?

Accepted Answer

Non-horizontal, non-vertical line with slope 2 and $$y-$$intercept $$-1$$

Question 13

Which of the following is the leading coefficient of $$f(x) = -4x^3$ + 2x^2$ - x + 5$$?

Accepted Answer

$$-4$$

Question 14

A quadratic function models the height $$h (in $$meters) of a ball thrown upward as $$h(t) = -4.9t^2$ + 20t + 1.5. $$What is the degree of this polynomial?

Accepted Answer

2

Question 15

Which of the following is a property of a linear function?

Accepted Answer

Its graph is a straight line with constant slope.

Question 16

If $$f(x) = (x - 2)^4$, what is the degree and leading coefficient of f(x$$)$$?

Accepted Answer

Degree: 4, Leading coefficient: 1

Question 17

Which of the following functions is linear?

Accepted Answer

$$f(x) = 2x - 1$$

Question 18

A horizontal line is represented by which type of polynomial function?

Accepted Answer

Constant function

Question 19

Which of the following is the correct domain of any polynomial function?

Accepted Answer

All real numbers

Question 20

If $$f(x) = 0$$ for all $$x$$, what is the name of this function?

Accepted Answer

Zero function

4.1 Polynomial Functions: Definitions, Properties, and Examples

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