I'm assuming the function is f(x) = (2x+8)/(x^2+5x+6). If so, make sure to use parenthesis to indicate that you're dividing all of "2x+8" over all of "x^2+5x+6" as one big fraction. Otherwise, things are ambiguous and it leads to confusion.

Side Note: x^2 means "x squared"

Factor the numerator: 2x+8 = 2(x+4)
Factor the denominator: x^2+5x+6 = (x+2)(x+3)

There are no common factors between the numerator and denominator. So there is nothing to cancel out.

Recall that you cannot divide by zero. Something like 1/0 is undefined.
We need to find the x values that cause the denominator to be zero.
Set the denominator equal to zero and solve for x
x^2+5x+6 = 0
(x+2)(x+3) = 0
x+2 = 0 or x+3 = 0
x = -2 or x = -3

The x values x = -2 or x = -3 will lead to the denominator being zero. This means that the vertical asymptotes are x = -2 or x = -3 as shown by the blue dashed vertical lines in the attached image.

4 0

3 years ago

Write 3 x 7 x 7 x 7 x 7 as a index notation

statuscvo [17]

Answer:

3 x 7 x 7 x 7 x 7

= 3 x $7^{4}$

7 0

2 years ago

A right come has a volume of 24pie cubic meters and a radius of 3 meters find the height of the cone

JulijaS [17]

Hello!

The equation for find the h when given volume and radius is

$h = 3 \frac{V}{ \pi r^{2} }$

h is height
v is volume
r is radius

Put in the values you know

$3 \frac{24 \pi }{ \pi 3^{2} }$

Since there is pi on the top and bottom we can get rid of it

multiply the 3 by the top number

$\frac{72}{9}$

the answer is 8m

Hope this helps!

4 0

3 years ago

Kim buys a new shirt for $25.50. She has to pay 8% sales tax. How much tax will be paid?​

Kim buys a new shirt for $25.50. She has to pay 8% sales tax. How much tax will be paid?