Functions of their graphs

• Jul 13th 2008, 05:26 PM
spinka
Functions of their graphs
F(x)= (x^2 + 2)/ (x + 4)

a) What is the domain of f?
b)List the x-intercepts, if any, of the graph of f.
c)List the y-intercept, if there is one, of the graph of f.

Thank you!
• Jul 13th 2008, 05:35 PM
o_O
(a) What x values can the function not have? Hint: Denominator = 0?

(b)To find the x-intercept, notice that the y-coordinate will be equal to 0. So set f(x) = 0 and solve for x, i.e.:
$\displaystyle 0 = \frac{x^{2} + 2}{x+4}$ (Can you even solve this? If not, what does that mean?)

(c) To find the y-intercept, notice that the x-coordinate will be equal to 0. So replace each x with a 0 and solve for f(0).
• Jul 13th 2008, 05:55 PM
spinka
a) -4
b) x-intercept = 0
c) y-intercept = 1/2

Are these values correct?
• Jul 13th 2008, 06:00 PM
o_O
Just to reiterate, what you got for (a) is the value you cannot have in your domain.

All is correct except for (b).

Remember that whatever you x-intercept is, it will have a y-coordinate of 0. If you plug in x = 0 into f(x), do you get 0?
• Jul 13th 2008, 06:07 PM
spinka
B) would the answer be undefined?

Thanks.
• Jul 13th 2008, 06:09 PM
o_O
Not undefined. Just that it doesn't exist! Since you can't find a solution, it means your graph doesn't have a x-intercept.