7. Polynomial Functions Facts

Multiple Choice

Which of the following best describes a continuous function?

• A function whose graph has no breaks

• A function whose graph has a break

• A function that crosses the x-axis only

• A function with only positive y-values

Multiple Choice

Which of the following best describes the domain and range of the function y = (x + 3)^3 + 2?

• Domain: All real numbers, Range: All real numbers

• Domain: x > 0, Range: y > 0

• Domain: x < 0, Range: y < 0

• Domain: x ≠ -3, Range: y ≠ 2

Multiple Choice

According to the definitions, an interval where as x increases, y decreases is called a(n) ___ interval.

• increasing

• decreasing

• constant

• undefined

Multiple Select

Which intervals describe where the function y = (x + 3)^3 + 2 is increasing? Select all that apply.

• (-∞, -3)

• (-3, ∞)

• (-∞, ∞)

• (-3, 3)

Multiple Choice

Which of the following statements best describes the extrema of the function y = (x + 3)^3 + 2 as shown in the graph?

• The function has a maximum but no minimum.

• The function has a minimum but no maximum.

• The function has neither a maximum nor a minimum.

• The function has both a maximum and a minimum.

Multiple Choice

Which point represents the minimum value of the function y = 2(x - 1)^4 - 2?

• (1, -2)

• (0, -2)

• (2, 0)

• (-1, 30)

Multiple Choice

If x = -1, what is the value of f(x) for the function y = (x + 3)^3 + 2?

• 2

• 10

• 8

• 0

Multiple Choice

If x = 2, find the value of f(x) for the function y = 2(x - 1)^4 - 2.

• 0

• 2

• -2

• 30

Multiple Choice

Which of the following best describes the end behavior of the function y = (x + 3)^3 + 2 as x approaches negative infinity and positive infinity?

• As x → -∞, y → -∞; As x → +∞, y → +∞

• As x → -∞, y → +∞; As x → +∞, y → -∞

• As x → -∞, y → 0; As x → +∞, y → 0

• As x → -∞, y → +∞; As x → +∞, y → +∞

Multiple Choice

Compare the end behavior of the functions y = (x + 3)^3 + 2 and y = 2(x - 1)^4 - 2. How do their left and right end behaviors differ?

• Both functions go up as x → -∞ and x → +∞

• The first goes down as x → -∞ and up as x → +∞; the second goes up as x → -∞ and up as x → +∞

• The first goes up as x → -∞ and down as x → +∞; the second goes down as x → -∞ and down as x → +∞

• Both functions go down as x → -∞ and x → +∞

Multiple Choice

Which of the following statements is true about the function y = (x + 3)^3 + 2 regarding its asymptotes?

• It has a vertical asymptote at x = -3

• It has a horizontal asymptote at y = 2

• It has no vertical or horizontal asymptotes

• It has both vertical and horizontal asymptotes

Multiple Select

Which of the following functions has neither vertical nor horizontal asymptotes?

• y = (x + 3)^3 + 2

• y = 2(x - 1)^4 - 2

• y = 1/(x - 2)

• y = e^x