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Chapter 6: Q. 38 (page 419)

graph each function. Be sure to label key points and show at least two cycles. Use the graph to determine the domain and the range of each function.

y=3cot12x-2

Short Answer

Expert verified

The domain of the function is{x|x鈮�蟺,kisaninteger}

The range of the function is (-鈭�,鈭�)

The graph of the function y=3cot12x-2is

Step by step solution

01

Step 1. Given data

The given function is

y=3cot12x-2

02

Step 2. Graph of the parent function

Parent function of y=3cot12x-2is y=cotx

Plot the graph of y=cot(x)

03

Step 3. Vertical stretch

Plot y=3cotxby vertical stretching the graph of y=cot(x)by a factor of 3

04

Step 4. Horizontal stretch 

Plot y=3cot12xby Horizontal stretching the graph of y=3cotxby a factor of 12

05

Step 5. Vertical shift

Plot y=3cot12x-2by vertical shifting the graph of y=3cot12xto downward by two units

06

Step 6. Domain and range

The graph of function state that the

The domain of the function y=3cot12x-2is localid="1646316950947" {x|x鈮�蟺,kisaninteger}

The range of the function y=3cot12x-2is(-鈭�,鈭�)

07

Step 7. Verification

Plot the graph of y=3cot12x-2using a graphing utility

The graph matches so our graph is correct.

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