Thread: 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!

(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.:
(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).

a) -4
b) x-intercept = 0
c) y-intercept = 1/2

Are these values correct?

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?

B) would the answer be undefined?

Thanks.

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.