Question

Evaluate the function for \(x=0,1,2,3,\) and 4. $$f(x)=x^{2}-1$$

Short answer

The computed function values are: \(f(0)=-1\), \(f(1)=0\), \(f(2)=3\), \(f(3)=8\), and \(f(4)=15\).

Step-by-step solution

Substituting \(x=0\)

To find the value of the function \(f(x)\) for \(x=0\), substitute 0 into the equation. \(f(0)=(0)^2 - 1 = 0 - 1 = -1\). The value of \(f(0)\) is -1

Substituting \(x=1\)

To calculate \(f(1)\), replace x with 1. \(f(1)=(1)^2 - 1 = 1 - 1 = 0\). Therefore, \(f(1)\) evaluates to 0.

Substituting \(x=2\)

Substitute 2 into the function \(f(x)\) - \(f(2)=(2)^2 - 1 = 4 - 1 = 3\). So the value of \(f(2)\) is 3.

Substituting \(x=3\)

Replace x with 3 in the function \(f(x)\) - \(f(3)=(3)^2 - 1 = 9 - 1 = 8\). Hence \(f(3)\) is 8.

Substituting \(x=4\)

Lastly, substitute 4 into the function \(f(x)\) - \(f(4)=(4)^2 - 1 = 16 - 1 = 15\). Therefore, \(f(4)\) is equal to 15.