Identify the discontinuities, graph, and find the zeros of the rational function
f(x) = (4x^2-36x)/(x-9)

Question

Identify the discontinuities, graph, and find the zeros of the rational function 
f(x) = (4x^2-36x)/(x-9)

anonymous · Answer

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

anonymous · Answer

when is this problem undefined

anonymous · Answer

got that part i just dont know what the point of discontinuity is...
all i know is that its going to bo (9,y)

anonymous · Answer

undefined?

anonymous · Answer

when is there an asymptote

anonymous · Answer

undefined is when you have a denominator that equals 0 or when a function is undefined such as ln(-1)

anonymous · Answer

9? x cant equal 9?

anonymous · Answer

yes so 9 is a discontinuity

anonymous · Answer

because at that point it breaks from the continuous line. it's an asymptote

now to find out if it's a removable discontinuity, simplify the problem... if you cancel out the (x-9)'s

anonymous · Answer

4x. but i thought the discontinuity was a specific point....

anonymous · Answer

it is so at x=9 you have the function 4x which is continuous for all real so now you have a piecewise function as such


|dw:1343692622097:dw|