Let's solve the problem step by step.
---
Objective:
Identify the type of function represented by each graph based on its shape and characteristics. We’ll use the
parent functions listed in the table:
| Name | Characteristics | Parent Function |
|------|------------------|-----------------|
| Constant Function | Straight horizontal line | $ y = a $ |
| Linear Function | Straight diagonal line | $ y = x $ |
| Absolute Value Function | Diagonal lines shaped like a V | $ y = |x| $ |
| Quadratic Function | Curved like a parabola | $ y = x^2 $ |
We'll analyze each graph from 1 to 6.
---
Exercise 1
Graph 1:
- It is a
straight diagonal line going upward from left to right.
- It passes through points like (-4, -4), (0, 0), (4, 4).
- This is a straight line with positive slope.
✔ Type: Linear Function
>
✔ Answer:
Linear Function
---
Exercise 2
Graph 2:
- The graph has a
V-shape, with two diagonal lines meeting at a point at the bottom.
- The vertex is at (0, -4), and it opens upward.
- This matches the
absolute value function pattern.
✔ Type: Absolute Value Function
>
✔ Answer:
Absolute Value Function
---
Exercise 3
Graph 3:
- The graph is a
U-shaped curve, symmetric about the y-axis.
- It opens
upward, and the vertex is at (0, 0).
- This is a classic
parabola.
✔ Type: Quadratic Function
>
✔ Answer:
Quadratic Function
---
Exercise 4
Graph 4:
- A
straight diagonal line going downward from left to right.
- It passes through (0, 0), (-2, 2), (2, -2), etc.
- Negative slope, but still a straight line.
✔ Type: Linear Function
>
✔ Answer:
Linear Function
---
Exercise 5
Graph 5:
- A
horizontal straight line at $ y = 2 $.
- No change in y-value as x changes.
✔ Type: Constant Function
>
✔ Answer:
Constant Function
---
Exercise 6
Graph 6:
- A
V-shaped graph, symmetric about the y-axis, with vertex at (0, 0).
- Opens upward, two straight lines forming a "V".
- Matches the
absolute value function.
✔ Type: Absolute Value Function
>
✔ Answer:
Absolute Value Function
---
✔ Final Answers:
| Exercise | Type of Function |
|--------|-------------------|
| 1 | Linear Function |
| 2 | Absolute Value Function |
| 3 | Quadratic Function |
| 4 | Linear Function |
| 5 | Constant Function |
| 6 | Absolute Value Function |
---
🔍 Explanation Summary:
-
Linear: Straight diagonal lines (positive or negative slope)
-
Constant: Horizontal straight lines
-
Absolute Value: V-shaped graphs
-
Quadratic: Parabolic curves (U-shaped)
By matching the shape of each graph to these key features, we can identify the correct parent function.
Let me know if you'd like help writing equations for any of these!
Parent Tip: Review the logic above to help your child master the concept of function transformation worksheet.
