Chapter 1.3, Problem 12E

To determine

To Find: Graph the function using the graphing utility and find the domain and range. Then find the domain and range algebraically.

Answer to Problem 12E

Domain: $(-\infty ,\infty )$

Range: $[-1,\infty )$

Explanation of Solution

Given: $f(x)=x^2-1$

Given: $f(x)=x^2-1$

The graph of the function is

  

From the graph it is seen that

Domain: $(-\infty ,\infty )$

Range: $[-1,\infty )$

Now

Algebraically

The function does not have any undefined points

Thus

Domain: $(-\infty ,\infty )$

Now finding range

For the parabola

  $a{x}^2+bx+c$

Here

  $f(x)=x^2-1$

  $a=1>0$

Vertex: $(0,-1)$

Thus

  $f(x)\ge -1$

Hence,

Domain: $(-\infty ,\infty )$

Range: $[-1,\infty )$