Question
Asked Oct 26, 2019

For the problem: f(x)=8/x^2-16

a. Please find the x and y intercepts

b. Test for symmetry: is the function even, odd, or neither?

c. Find the vertical asymptotes

Thank you in advance!

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Expert Answer

Step 1

Given function is

8
f(x)
x-16
help_outline

Image Transcriptionclose

8 f(x) x-16

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Step 2

For x and y intercept

take x 0
8
f(0)
=
-16
1
f(0)
-2
(
is y intercept
0,
2
for x intercept, take f(x)= 0
=0
x2-16
8 -0x(x2 -16)
no x intercept
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Image Transcriptionclose

take x 0 8 f(0) = -16 1 f(0) -2 ( is y intercept 0, 2 for x intercept, take f(x)= 0 =0 x2-16 8 -0x(x2 -16) no x intercept

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Step 3

For even odd...

replace x by -x
f(-x)
(-x)216
f(-x)
x2-16
f(-x)f(x)
function is even
help_outline

Image Transcriptionclose

replace x by -x f(-x) (-x)216 f(-x) x2-16 f(-x)f(x) function is even

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