Question

choose the function that represents the data in the table
x | 0 | 1 | 2 | 3 | 4 | 5
f(x) | -3 | -1 | 1 | 3 | 5 | 7
options:

• ( f(x)=\frac{2}{x}-3 )
• ( f(x)=2x - 3 )
• ( f(x)=x^2 - 3 )
• ( f(x)=2x^2 - 3 )

Explanation:

Step1: Test x=0 in each function

For $f(x)=\frac{2}{x}-3$: Undefined (division by 0, eliminate)
For $f(x)=2x-3$: $2(0)-3=-3$ (matches table)
For $f(x)=x^2-3$: $0^2-3=-3$ (matches table)
For $f(x)=2x^2-3$: $2(0)^2-3=-3$ (matches table)

Step2: Test x=1 in remaining functions

For $f(x)=2x-3$: $2(1)-3=-1$ (matches table)
For $f(x)=x^2-3$: $1^2-3=-2$ (does not match, eliminate)
For $f(x)=2x^2-3$: $2(1)^2-3=-1$ (matches table)

Step3: Test x=2 in remaining functions

For $f(x)=2x-3$: $2(2)-3=1$ (matches table)
For $f(x)=2x^2-3$: $2(2)^2-3=5$ (does not match, eliminate)

Step4: Verify with remaining x values

For $x=3$: $2(3)-3=3$ (matches)
For $x=4$: $2(4)-3=5$ (matches)
For $x=5$: $2(5)-3=7$ (matches)

Answer:

$f(x)=2x-3$