Question

1. a table has input values $x=1,2,3,4$ and output values $y=3,5,7,9$. what is the rule for this function?

a. $y=x+1$
b. $y=2x+1$
c. $y=x+2$
d. $y=x^2$

Explanation:

Step1: Test option a with x=1

Substitute $x=1$ into $y=x+1$:
$y=1+1=2$ (does not match output 3)

Step2: Test option b with x=1

Substitute $x=1$ into $y=2x+1$:
$y=2(1)+1=3$ (matches output 3)

Step3: Verify option b with x=2

Substitute $x=2$ into $y=2x+1$:
$y=2(2)+1=5$ (matches output 5)

Step4: Verify option b with x=3

Substitute $x=3$ into $y=2x+1$:
$y=2(3)+1=7$ (matches output 7)

Step5: Verify option b with x=4

Substitute $x=4$ into $y=2x+1$:
$y=2(4)+1=9$ (matches output 9)

Step6: Eliminate remaining options

Test x=1 in c: $y=1+2=3$, but x=2 gives $y=4$ (does not match 5). Test x=1 in d: $y=1^2=1$ (does not match 3).

Answer:

b. $y=2x+1$