Note that this graph has a zero at x = 1 and a vertical asymptote at x = -4. Only Answer (e) corresponds to that. Try letting x = 1. y is zero, correct? Try letting x = -4. y is undefined, correct?

7 0

3 years ago

What are the zero(s) of the function f(x)=<img src="https://tex.z-dn.net/?f=%5Cfrac%7B4x%5E%7B2%7D-36x%20%7D%7Bx-9%7D" id="TexFo

Contact [7]

Answer:

Step-by-step explanation:

The function will be zero when the numerator is equal to 0. So, set the numerator equal to 0 and solve:

$0 = 4 {x}^{2} - 36x$

I will use the quadratic formula:

$\frac{ 36 + \sqrt{ {36}^{2} - 4(4)(0)} }{2(4)} \\ \frac{ 36 + 36}{8} = 9$

Therefore, x = 9 is a 0. Let's check with subtracted root now:

$\frac{ 36 - \sqrt{ {36}^{2} - 4(4)(0)} }{2(4)} \\ \frac{ 36 - 36}{8} = 0$

It appears 0 is also a root.

Therefore, the answer is D.

7 0

3 years ago