How do you graph $f (x) = \frac{x^{2} - 100}{x + 10}$ $f(x)= (x^2-100)/(x+10)$ ?

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How do you graph $f (x) = \frac{x^{2} - 100}{x + 10}$ $f(x)= (x^2-100)/(x+10)$ ?

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Answer 1 · 2015-06-28T16:08:06

$f (x) = \frac{x^{2} - 100}{x + 10} = \frac{(x - 10) (x + 10)}{x + 10} = x - 10$ $f(x) = (x^2-100)/(x+10) = ((x-10)(x+10))/(x+10) = x-10$

with excluded value $x = - 10$ $x=-10$ .

This is a straight line of slope $1$ $1$ passing through $(0, - 10)$ $(0, -10)$ and $(10, 0)$ $(10, 0)$ with excluded point $(- 10, - 20)$ $(-10, -20)$

Explanation:

$f (x) = \frac{x^{2} - 100}{x + 10}$ $f(x) = (x^2-100)/(x+10)$

$= \frac{(x - 10) (x + 10)}{x + 10}$ $= ((x-10)(x+10))/(x+10)$

$= x - 10$ $= x-10$

with exclusion $x \neq - 10$ $x!=-10$ .

The graph of $f (x)$ $f(x)$ is like the graph of $x - 10$ $x-10$ except that $f (x)$ $f(x)$ is not defined at the point $(- 10, - 20)$ $(-10, -20)$

All the limits as you approach that point behave well, it's just that $f (- 10)$ $f(-10)$ is undefined as it's equal to $\frac{0}{0}$ $0/0$ .

graph{(x^2-100)/(x+10) [-37.5, 42.5, -24, 16]}

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How do you graph $f (x) = \frac{x^{2} - 100}{x + 10}$ $f(x)= (x^2-100)/(x+10)$ ?

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