Question

Match the description with the correct Function.

Function A:

Function B:

x y
0 1
4 9
8 17


Function C: y=x+20

Answer 1

To match the descriptions with the correct function, let's analyze the given data for Function A and Function B, and then compare them to Function C.

### Analysis of Function A (x, y)
- \( (0, 1) \): When \( x = 0 \), \( y = 1 \)
- \( (4, 9) \): When \( x = 4 \), \( y = 9 \)
- \( (8, 17) \): When \( x = 8 \), \( y = 17 \)

### Analyzing the pattern:
1. From the points:
- At \( x = 0, y = 1 \)
- At \( x = 4, y = 9 \) (Increase by 8)
- At \( x = 8, y = 17 \) (Increase by 8)

2. The difference in \( y \) values is consistent and suggests a linear relationship.

### Finding the function:
A simple function in the form of \( y = mx + b \) would be suitable. Let's solve for \( m \) and \( b \).

- From the two points:
- From (0,1): \( b = 1 \)
- Assuming \( y = mx + 1 \)
- Using (4,9): \( 9 = 4m + 1 \) → \( 8 = 4m \) → \( m = 2 \)

Thus, Function A appears to be represented as:
\[ y = 2x + 1 \]

### Now looking at Function B:
We don't have specific values, so let's assume it’s an unknown relationship.

### Function C: \( y = x + 20 \)
This is a linear function where each \( x \) translates to \( y \) simply by adding 20.

### Conclusions:
1. **Function A** corresponds to \( y = 2x + 1 \).
2. **Function C** is clearly \( y = x + 20 \).
3. **Function B** would then imply some other function not in your data, possibly with a different linear slope than Function A.

In summary, we have:
- Function A: \( y = 2x + 1 \) (matches the given point data),
- Function C: \( y = x + 20 \) (directly given),
- Function B: assumed to be different and does not have data provided in your context.

Thus, if I were to match based only on the description provided, the matches would be:
- Function A: \( y = 2x + 1 \) (based on points),
- Function C: \( y = x + 20 \).
- Function B would not be specifically identified without additional description.