Question

Which of the following equations correctly describes the function in the table using function notation? x y 0 -2 2 4 4 10 6 16 (1 point) Responses f(x)=x−2 f of x is equal to x minus 2 f(x)=2x f of x is equal to 2 x f(x)=3x−2 f of x is equal to 3 x minus 2 f(x)=2x+4

Answer 1

To determine which equation correctly describes the function in the table, we need to analyze the given pairs of \( (x, y) \):

- When \( x = 0 \), \( y = -2 \)
- When \( x = 2 \), \( y = 4 \)
- When \( x = 4 \), \( y = 10 \)
- When \( x = 6 \), \( y = 16 \)

We'll test each proposed function to confirm which one fits the values in the table.

1. **For \( f(x) = x - 2 \)**:
- \( f(0) = 0 - 2 = -2 \) (correct)
- \( f(2) = 2 - 2 = 0 \) (incorrect, should be 4)
- This function does not match.

2. **For \( f(x) = 2x \)**:
- \( f(0) = 2(0) = 0 \) (incorrect, should be -2)
- This function does not match.

3. **For \( f(x) = 3x - 2 \)**:
- \( f(0) = 3(0) - 2 = -2 \) (correct)
- \( f(2) = 3(2) - 2 = 6 - 2 = 4 \) (correct)
- \( f(4) = 3(4) - 2 = 12 - 2 = 10 \) (correct)
- \( f(6) = 3(6) - 2 = 18 - 2 = 16 \) (correct)
- This function matches all points.

4. **For \( f(x) = 2x + 4 \)**:
- \( f(0) = 2(0) + 4 = 4 \) (incorrect, should be -2)
- This function does not match.

The correct function that describes the relationship in the table is:

**\( f(x) = 3x - 2 \)**