Question

which function is represented by this table?
x | y
1 | 4
2 | 5
3 | 6
4 | 7
5 | 8
a. $y = x + 1$
b. $y = 2x$
c. $y = 4x$
d. $y = x + 3$

Explanation:

Step1: Test Option A

Substitute \(x = 1\) into \(y=x + 1\), we get \(y=1 + 1=2\), but the table has \(y = 4\) when \(x = 1\), so A is wrong.

Step2: Test Option B

Substitute \(x = 1\) into \(y = 2x\), we get \(y=2\times1 = 2\), but the table has \(y = 4\) when \(x = 1\), so B is wrong.

Step3: Test Option C

Substitute \(x = 1\) into \(y = 4x\), we get \(y=4\times1=4\), substitute \(x = 2\) into \(y = 4x\), we get \(y = 4\times2=8\), but the table has \(y = 5\) when \(x = 2\), so C is wrong.

Step4: Test Option D

Substitute \(x = 1\) into \(y=x + 3\), we get \(y=1+3 = 4\) (matches the table). Substitute \(x = 2\) into \(y=x + 3\), we get \(y=2 + 3=5\) (matches). Substitute \(x = 3\) into \(y=x + 3\), we get \(y=3+3 = 6\) (matches). Substitute \(x = 4\) into \(y=x + 3\), we get \(y=4+3 = 7\) (matches). Substitute \(x = 5\) into \(y=x + 3\), we get \(y=5+3 = 8\) (matches). So D is correct.

Answer:

D. \(y = x + 3\)