Looking at the image, I can see four different graphs with questions about whether they are linear or nonlinear, and other properties like intercepts, symmetry, and intervals of increase/decrease.
Let me work through each graph systematically:
1. David's Savings for Car (Linear Graph)
- This is a straight line going up
- y-intercept: 1400 (where it crosses the y-axis)
- No x-intercept shown (doesn't cross x-axis in the visible range)
- Not symmetric (lines aren't symmetric unless horizontal/vertical)
- Always increasing (going up from left to right)
- Never decreasing
- No relative extrema (no peaks or valleys)
2. Height of Golf Ball (Parabola - Nonlinear)
- This is a curved line (parabola opening downward)
- x-intercepts: 0 and 120 (where it crosses x-axis)
- y-intercept: 0 (starts at origin)
- Has line symmetry at x = 60 (middle of 0 and 120)
- Increasing when 0 < x < 60 (going up to the peak)
- Decreasing when 60 < x < 120 (going down from the peak)
- Relative maximum at x = 60
3. Right Whale Population (Linear Graph)
- This is a straight line going down
- x-intercept: 10 (where it crosses x-axis)
- y-intercept: 240 (where it crosses y-axis)
- Not symmetric
- Never increasing
- Always decreasing when x > 0
- No relative extrema
4. Gateway Arch (Parabola - Nonlinear)
- This is a curved line (parabola opening downward)
- x-intercepts: -320 and 320 (where it crosses x-axis)
- y-intercept: 640 (where it crosses y-axis)
- Has line symmetry at x = 0 (middle of -320 and 320)
- Increasing when -320 < x < 0 (going up to the peak)
- Decreasing when 0 < x < 320 (going down from the peak)
- Relative maximum at x = 0
Final Answer:
David's Savings: Linear, y-int: 1400, increasing for all x, no symmetry
Golf Ball: Nonlinear, x-int: 0 and 120, y-int: 0, symmetric at x=60, increasing: 0<x<60, decreasing: 60<x<120
Whale Population: Linear, x-int: 10, y-int: 240, decreasing for x>0, no symmetry
Gateway Arch: Nonlinear, x-int: -320 and 320, y-int: 640, symmetric at x=0, increasing: -320<x<0, decreasing: 0<x<320
Parent Tip: Review the logic above to help your child master the concept of interpreting graphs.
