How do you graph $f (x) = \frac{4 x^{2} - 36 x}{x - 9}$ $f(x) = (4x^2-36x) / (x-9)$ ?

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How do you graph $f (x) = \frac{4 x^{2} - 36 x}{x - 9}$ $f(x) = (4x^2-36x) / (x-9)$ ?

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Answer 1 · 2018-04-22T19:12:08

see below

Explanation:

you can first simplify this expression:

$4 x^{2} - 36 x = 4 x (x - 9)$ $4x^2 - 36x = 4x(x-9)$

$\frac{4 x^{2} - 36 x}{x - 9} = \frac{4 x (x - 9)}{x - 9} = 4 x$ $(4x^2-36x)/(x-9) = (4x(x-9))/(x-9) = 4x$

therefore, for all points where $\frac{4 x^{2} - 36 x}{x - 9}$ $(4x^2-36x)/(x-9)$ can be defined, you'll get a graph of $f (x) = 4 x$ $f(x)= 4x$ .

however, not all points can be defined.

any number divided by zero is undefined. this means that the $x$ $x$ -value where the denominator $x - 9$ $x-9$ is $0$ $0$ is also undefined.

when $x - 9 = 0$ $x-9 = 0$ , $x = 9$ $x = 9$ .

this means that the line cannot touch any point where $x = 9$ $x = 9$ .

however, in all other ways, it will look like the graph of $f (x) = 4 x$ $f(x) = 4x$ .

this gives a straight line with gradient $4$ $4$ , and with a hole where the point on the $x$ $x$ -axis is $9$ $9$ :

graph{(4x^2-36x)/(x-9) [2.7, 22.7, 32.56, 42.56]}

if you scroll along the graph, you'll see a directly proportional relationship between $x$ $x$ and $y$ $y$ , where the $y$ $y$ -coordinate is $4$ $4$ times the $x$ $x$ -coordinate.

if you scroll up to where $x = 9$ $x=9$ , you'll see that the coordinates are
( $9$ $9$ , undefined).

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How do you graph $f (x) = \frac{4 x^{2} - 36 x}{x - 9}$ $f(x) = (4x^2-36x) / (x-9)$ ?

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Explanation:

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How do you graph f(x)=4x2−36xx−9f(x) = (4x^2-36x) / (x-9)?

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How do you graph $f (x) = \frac{4 x^{2} - 36 x}{x - 9}$ $f(x) = (4x^2-36x) / (x-9)$ ?