Question

$x$	$f\left(x\right)$
$-3$	$8$
$-2$	$3$
$-1$	$0$
$0$	$-1$
$1$	$0$

Which of the following equations describes the chart above?

• A. $f\left(x\right)=x-x^2$
• B. $f\left(x\right)=x-1$
• C. $f\left(x\right)=x^2-1$
• D. $f\left(x\right)=x^2+1$

Answer 1

Answer: (C)

$f\left(x\right)=x^2-1$

For this kind of problem, first check the options:
First option: $f\left(x\right)=x-x^2$
When you put x = -3 in the function f(x)
$f(-3)=-3-(-3{)}^2=-3-9=-12\ne 8$ in the chart.
Second option: $f\left(x\right)=x-1$
When you put x = -3 in the function f(x)
$f(-3)=-3-1=-4\ne 8$ in the chart.
Third option: $f\left(x\right)=x^2-1$
When you put x = -3 in the function f(x)
$f(-3)=(-3{)}^2-1=9-1=8=8$ in the chart.
Therefore, the equation $f\left(x\right)=x^2-1$ describes the chart above.