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Finite Mathematics and Applied Cal...

7th Edition
Stefan Waner + 1 other
ISBN: 9781337274203

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BuyFindarrow_forward

Finite Mathematics and Applied Cal...

7th Edition
Stefan Waner + 1 other
ISBN: 9781337274203
Textbook Problem

In Exercises 33–42, use a graph to determine whether the given function is continuous on its domain. If it is not continuous on its domain, list the points of discontinuity. [HINT: See Example 1.]

f ( x ) = { x + 2       if  x < 0 2 x 1      if  x 0

To determine

Whether the function f(x)={x+2, if x<02x1, if x0 is continuous on its domain using the graph and give the points of discontinuity if it is not continuous on its domain.

Explanation

Given information:

The provided function is f(x)={x+2, if x<02x1, if x0.

Consider the function, f(x)={x+2, if x<02x1, if x0

To draw the graph of f(x)={x+2, if x<02x1, if x0, first compute the value of f(x) for different values of x.

Compute the value of f(x) at x=1 by substituting x=1 in the equation f(x)=x+2 as,

f(1)=1+2=1

Compute the value of f(x) at x=3 by substituting x=3 in the equation f(x)=x+2 as,

f(3)=3+2=1

Compute the value of f(x) at x=0 by substituting x=0 in the equation f(x)=2x1 as,

f(0)=2(0)1=1

Compute the value of f(x) at x

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