   Chapter 1.6, Problem 3E

Chapter
Section
Textbook Problem

Determining Continuity In Exercises 1-10, determine whether the function is continuous on the entire real number line. Explain your reasoning. See Examples 1 and 2. f ( x ) = 3 x 2 − 16

To determine

The continuity of function f(x)=3x216.

Explanation

Given Information:

The provided function is f(x)=3x216.

Consider the provided function, f(x)=3x216.

The function f(x)=3x216 is a rational function. The domain of this rational function is all the real number except 4 and 4 because the function f(x)=3x216 is not defined at these values.

Now, choose some values for x and compute the value for f(x), in order to form the ordered pairs that will plot on the graph.

So, put x=1 in the provided expression,

f(1)=3(1)216=3116=315=0.2

Now, put x=0,

f(0)=3(0)216=3016=316

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