Question

The table below represents a function.

x y
0 1
2 5
5 26
7 50
Which equation makes the table true?

f( x) = 2 x - 1
f( x) = 2 x + 1
f( x) = x^2 + 1
f( x) = ^ 2 - 1

Answer 1

To find the equation that describes the function represented in the table, we can test each of the proposed equations using the x-values from the table to see which one yields the corresponding y-values.

1. **f(x) = 2x - 1**
- f(0) = 2(0) - 1 = -1 (not 1)
- f(2) = 2(2) - 1 = 3 (not 5)
- f(5) = 2(5) - 1 = 9 (not 26)
- f(7) = 2(7) - 1 = 13 (not 50)

This equation does not match.

2. **f(x) = 2x + 1**
- f(0) = 2(0) + 1 = 1 (matches)
- f(2) = 2(2) + 1 = 5 (matches)
- f(5) = 2(5) + 1 = 11 (not 26)
- f(7) = 2(7) + 1 = 15 (not 50)

This equation does not match.

3. **f(x) = x^2 + 1**
- f(0) = 0^2 + 1 = 1 (matches)
- f(2) = 2^2 + 1 = 5 (matches)
- f(5) = 5^2 + 1 = 26 (matches)
- f(7) = 7^2 + 1 = 50 (matches)

All values match! This equation is indeed correct.

4. **f(x) = x^2 - 1**
- f(0) = 0^2 - 1 = -1 (not 1)
- f(2) = 2^2 - 1 = 3 (not 5)
- f(5) = 5^2 - 1 = 24 (not 26)
- f(7) = 7^2 - 1 = 48 (not 50)

This equation does not match.

Based on our checks:

The correct equation that makes the table true is:
**f(x) = x^2 + 1**.