Question

Determine the y-intercept, if it exists. If the function has no y-intercept, explain how the equation is used to determine this.

a) k(x) = log5(x - 5)

b) g(x) = x - 1 / x + 2

Determine the x-intercept, if it exists. If the function has no x-intercept, explain how the equation is used to determine this.

a) f(x) = 2x^2 + 10x + 8

b) g(x) = x - 1 / x + 2

Answer 1

Explanation:

To find y-intercepts, we make x = 0

So for (a), log5(0-5) = log5(-5).

As the log of a negative number is undefined, then this graph has no y-intercept. (Im assuming log5 means log base 5)

Using the same method for (b) we get y = -1/2 for the intercept.

As for x-intercepts, make y=0. Part (a) requires some factorising but divide by 2 first.