Question

examples 1 and 2 additional practice use the graph to estimate the x - and y - intercepts of the function and describe where the function is positive and negative. 1. 2. 3.

Explanation:

Step1: Find x - intercepts

The x - intercepts are the points where the graph crosses the x - axis (y = 0).

Step2: Find y - intercepts

The y - intercepts are the points where the graph crosses the y - axis (x = 0).

Step3: Determine positive and negative intervals

A function is positive when y>0 and negative when y < 0.

For graph 1:

• x - intercepts: The graph crosses the x - axis at approximately x=-2 and x = 2.
• y - intercept: The graph crosses the y - axis at approximately y=-1.
• Positive and negative: The function is positive when - 2<x<2 (above the x - axis) and negative when x < - 2 or x>2 (below the x - axis).

For graph 2:

• x - intercepts: The graph crosses the x - axis at approximately x=-1 and x = 1.
• y - intercept: The graph crosses the y - axis at y = 0.
• Positive and negative: The function is positive when x < - 1 or x>1 (above the x - axis) and negative when - 1<x<1 (below the x - axis).

For graph 3:

• x - intercepts: The graph crosses the x - axis at x = 0.
• y - intercept: The graph crosses the y - axis at y = 0.
• Positive and negative: The function is positive when x>0 (above the x - axis) and negative when x < 0 (below the x - axis).

Answer:

For graph 1: x - intercepts: x≈ - 2,x≈2; y - intercept: y≈ - 1; Positive: - 2<x<2; Negative: x < - 2 or x>2.
For graph 2: x - intercepts: x≈ - 1,x≈1; y - intercept: y = 0; Positive: x < - 1 or x>1; Negative: - 1<x<1.
For graph 3: x - intercept: x = 0; y - intercept: y = 0; Positive: x>0; Negative: x < 0.