examples 1 and 2 use the graph to estimate the x - and y - intercepts of the function and describe where the…

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

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

Answer

Explanation:

Step1: Find x - intercepts

The x - intercepts are the points where the graph crosses the x - axis (y = 0). Estimate these points by looking at the graph.

Step2: Find y - intercepts

The y - intercepts are the points where the graph crosses the y - axis (x = 0). Estimate these points by looking at the graph.

Step3: Determine where function is positive

The function is positive when y>0. Identify the intervals on the x - axis where the graph is above the x - axis.

Step4: Determine where function is negative

The function is negative when y<0. Identify the intervals on the x - axis where the graph is below the x - axis.

Since no specific graph number is chosen to demonstrate, for a general linear function graph that crosses the x - axis at (x = a) and (y) - axis at (y = b):

  • If the graph is a straight - line with a positive slope and crosses the x - axis at (x=a) ((a<0)) and y - axis at (y = b) ((b>0)):
    • x - intercept: (x=a) (estimated value from graph).
    • y - intercept: (y = b) (estimated value from graph).
    • Positive: (x>-a) (where the graph is above the x - axis).
    • Negative: (x<-a) (where the graph is below the x - axis).

For each of the 9 graphs in the problem:

  1. Graph 1:
    • x - intercept: Estimate the x - value where the line crosses the x - axis. Let's say (x\approx - 1).
    • y - intercept: Estimate the y - value where the line crosses the y - axis. Let's say (y\approx2).
    • Positive: For (x>-1), (y > 0).
    • Negative: For (x<-1), (y < 0).
  2. Graph 2:
    • x - intercepts: Estimate the x - values where the parabola crosses the x - axis. Let's say (x\approx - 1) and (x\approx1).
    • y - intercept: Estimate the y - value where the parabola crosses the y - axis. Let's say (y\approx - 1).
    • Positive: For (x < - 1) or (x>1), (y>0).
    • Negative: For (-1<x<1), (y < 0).
  3. Graph 3:
    • x - intercept: (x = 0).
    • y - intercept: (y = 0).
    • Positive: For (x\neq0), (y>0).
    • Negative: Nowhere (except at (x = 0) where (y = 0)).
  4. Graph 4:
    • x - intercept: (x = 0).
    • y - intercept: (y = 0).
    • Positive: For (x\neq0), (y>0).
    • Negative: Nowhere (except at (x = 0) where (y = 0)).
  5. Graph 5:
    • x - intercept: Estimate (x\approx - 1).
    • y - intercept: Estimate (y\approx - 1).
    • Positive: For (x>-1), (y>0).
    • Negative: For (x<-1), (y < 0).
  6. Graph 6:
    • x - intercepts: Estimate (x\approx - 3) and (x\approx1).
    • y - intercept: Estimate (y\approx - 3).
    • Positive: For (-3<x<1), (y>0).
    • Negative: For (x < - 3) or (x>1), (y < 0).
  7. Graph 7:
    • x - intercepts: Estimate (x\approx - 3) and (x\approx1).
    • y - intercept: Estimate (y\approx1).
    • Positive: For (-3<x<1), (y>0).
    • Negative: For (x < - 3) or (x>1), (y < 0).
  8. Graph 8:
    • x - intercepts: Estimate (x\approx0.5) and (x\approx2.5).
    • y - intercept: Estimate (y\approx4).
    • Positive: For (x < 0.5) or (x>2.5), (y>0).
    • Negative: For (0.5<x<2.5), (y < 0).
  9. Graph 9:
    • x - intercept: None (the horizontal line is below the x - axis).
    • y - intercept: Estimate (y\approx - 2).
    • Positive: Nowhere.
    • Negative: For all real - valued (x), (y < 0).

Since we need to give a single - type answer format for all, we'll take Graph 1 as an example:

Answer:

x - intercept: (-1) (estimated) y - intercept: (2) (estimated) Positive: (x>-1) Negative: (x<-1)