For the given function f(x) = (x² -64) / (8x -64) there is no vertical asymptotes of the graph.
What is vertical asymptotes ?
"A vertical asymptote is a vertical line, , which represents that invisible line approaches from either the positive or negative side, the function approaches infinity. Vertical asymptotes occur at the values where a rational function has a denominator of 0."
According to the question,
Given,
f(x) = (x² -64) / (8x -64)
= ( x- 8)(x + 8) / 8(x -8)
= (x + 8) / 8
= x/8 + 1
To find vertical asymptotes denominator = 0.
But here denominator 8 ≠ 0
Therefore,
No vertical asymptotes
horizontal asymptotes: no
slant/ oblique asymptotes: y = x/8 + 1
Hence, the graph has no vertical asymptotes.
Learn more about vertical asymptotes here
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