Domain, Range, Intervals, Zeros and Intercepts

Select all the intervals that represent where the graph is decreasing.

What is another name for zeros?

What are the relative maximum and minimum values for the graph? (check all that apply)

Use the graph to identify the y-intercept and zeros.

• y-int: (0, -16),

  zero: (-2, 0), (2, 0)

• y-int: (16,0),

  zero: no zeros

• y-int: (0, -2), (0, 2), zero: (-16, 0)

• y-int: (-16, 0),

  zero: (0, -2), (0, 2)

Use the graph to determine the domain and range of the function.

• [0,-2]

• [0,4]

• [-4,0]

• [-2,0]

Determine whether the graph is that of a function. If it is, use the graph to find its domain and range, the intercepts, if any, and any symmetry with respect to the x-axis, y-axis, or the origin.

• Not a function

For the polynomial, list each real zero and its multiplicity. Determine whether the graph crosses or touches the x-axis at each x -intercept. f(x) = 4(x + 7)(x - 5)²

• -7, multiplicity 1, crosses x-axis; 5, multiplicity 2, touches x-axis

• 7, multiplicity 1, touches x-axis; -5, multiplicity 2, crosses x-axis

• -7, multiplicity 1, touches x-axis; 5, multiplicity 2, crosses x-axis

• 7, multiplicity 1, crosses x-axis; -5, multiplicity 2, touches x-axis

Find the x- and y-intercepts of f. f(x) = (x + 1)(x - 8)(x - 1)²

• x-intercepts: -1, 1, -8; y-intercept: 8

• x-intercepts: -1, 1, 8; y-intercept: -8

• x-intercepts: -1, 1, 8; y-intercept: 8

• x-intercepts: -1, 1, -8; y-intercept: -8

Use the x-intercepts to find the intervals on which the graph of f is above and below the x-axis. f(x) = (x + 2)³

• above the x-axis: (-∞, -2), (-2, ∞)

  below the x-axis: no intervals

• above the x-axis: (-∞, -2)

  below the x-axis: (-2, ∞)

• above the x-axis: no intervals

  below the x-axis: (-∞, -2), (-2, ∞)

• above the x-axis: (-2, ∞)

  below the x-axis: (-∞, -2)