Even or Odd symmetryWhat type of symmetry does the function y = 1 | x | have? Specify the intervals over which the function is increasing and the intervals where it is decreasing.

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Even or Odd symmetryWhat type of symmetry does the function   y  =      1                  |            x              |             have? Specify the intervals over which the function is increasing and the intervals where it is decreasing.

hrikalegt15 · Accepted Answer

Step 1Plotting the function is a good way to guess at where the function is going to be increasing or decreasing. Then you can think about why.Step 2As you increase x, what is going to happen to       1                  |            x              |            ? What happens when x approaches (but does not equal!) 0?

Rocco Juarez · Accepted Answer

Step 1Let   f  (  x  )  =  yLet&#039;s look at the function,   f  (  x  )  =      1    x  . Now, a function is even if:   f  (  −  x  )  =  f  (  x  ) and a function is odd if:  f  (  −  x  )  =  −  f  (  x  )Step 2We therefore can see that this function is an odd function, since;  f  (  −  x  )  =      1          −      x        =  −      1    x    =  −  f  (  x  )Now, the absolute value is defined as       |    x      |    =            x      2      With this in mind, let&#039;s look at your function;  f  (  x  )  =      1                  |            x              |            Now what happens when we look at   f  (  −  x  )?  f  (  −  x  )  =      1                  |            −      x              |              =      1          (      −      x              )        2              =      1                  x        2              =      1                  |            x              |              =  f  (  x  )Thus,   f  (  x  )  =      1                  |            x              |             is an even function, symmetric about the y-axis.

What type of symmetry does the function y=1/|x| have?

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