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Chapter 14: Q. 27 (page 906)

Is f continuous at 4?

Short Answer

Expert verified

f(x) is continuous atx=4.

Step by step solution

01

Step 1. Graph the function f(x)

Let us graph f(x)with the help of a graphing utility.

02

Step 2. Determine f(x) is continuous at  x=4

For a function to be continuous atx=c, then the function must be defined at x=candlimx鈫�c-f(x)=limx鈫�c+f(x)=f(c).

Let us consider the behavior of f(x)near x=0.

When we consider the limit coming from the left side, the function approaches a value of 4.

That islimx鈫�4-f(x)=4

When we consider the limit coming from the right side, the function approaches a value of 4.

That islimx鈫�4+f(x)=4

Sincelimx鈫�4-f(x)=limx鈫�4+f(x)=f(4), f(x)is continuous at 4.

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