Question

Which tables and graphs represent functions? Select all that apply.


Graph 1

x y
−3 25
−2 10
−1 7
0 6
1 7
2 10
3 25

Graph 2

x y
−3 −15
−2 −15
−1 −15
0 −15
1 −15
2 −15
3 −15

Answer 1

To determine which tables and graphs represent functions, we must check if each value of \( x \) has exactly one corresponding value of \( y \).

1. **Graph 1:**

- The values of \( y \) corresponding to different values of \( x \) are:
- For \( x = -3 \), \( y = 25 \)
- For \( x = -2 \), \( y = 10 \)
- For \( x = -1 \), \( y = 7 \)
- For \( x = 0 \), \( y = 6 \)
- For \( x = 1 \), \( y = 7 \)
- For \( x = 2 \), \( y = 10 \)
- For \( x = 3 \), \( y = 25 \)

- Each \( x \) value has a unique \( y \) value, so **Graph 1 represents a function.**

2. **Graph 2:**

- The values of \( y \) for different values of \( x \) are:
- For \( x = -3 \), \( y = -15 \)
- For \( x = -2 \), \( y = -15 \)
- For \( x = -1 \), \( y = -15 \)
- For \( x = 0 \), \( y = -15 \)
- For \( x = 1 \), \( y = -15 \)
- For \( x = 2 \), \( y = -15 \)
- For \( x = 3 \), \( y = -15 \)

- Although the values of \( y \) are the same for all \( x \) values, each \( x \) still corresponds to only one \( y \) value. Hence, **Graph 2 also represents a function.**

In conclusion, both Graph 1 and Graph 2 represent functions.