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Chapter 5: Q. 52 (page 284)

Use transformations to graph the function. Determine the domain, range and horizontal asymptote of the function.

fx=1-2-x/3

Short Answer

Expert verified

The graph of the function is given below,

Domain: All real numbers.

Range: y|y<1or-鈭�,1

Horizontal asymptote:y=1

Step by step solution

01

Step 1. Given information.

Consider the given function,

fx=1-2-x/3

First, plot the graph of localid="1646154462388" y=2x, then replace x by -x/3 and reflect about the y-axis.

Again, multiply it by localid="1646155262865" -1 and reflect about the x-axis.

Then add 1and shift up by 1unit,

02

Step 2. Determine the characteristics of the function.

Consider the given function,

fx=1-2-x/3

From the graph, the domain of the function is all real numbers. Then,

x鈫�鈭�,fx鈫�1

The range is -鈭�,1.

Horizontal asymptote is y=1.

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