Consider f(x) = log2(3-x).

Question

(a) Determine the domain of f.

(b) Find the y-intercept of f.

(c) Sketch the graph of f. Identify two other points on the graph.

Answer 1

Hi Sam,

(a) The domain of the function f(t)=log(t) is given by the condition t>0. So the whole argument of the logarithm, here denoted by t, must be positive.

In your case, you have log2(3-x) and hence you must impose 3-x>0 which implies x<3. So the domain is given by all real numbers less than 3.

(b) The y-intercept is given by considering the values of the function at the point x=0.

In your case, at x=0 you obtain f(0)=log2(3-0)=log2(3) which is the y-intercept

(c) One point is given by the x-intercept (y=0) which can be obtained by imposing the argument of the logarithm equal to 1. In your case, you have 3-x=1 which implies x=2. So another point is given by (2,0).

Another point can be evaluated by considering x=1 which has y-coordinate equal to log2(3-1)=log2(2).

I hope it helped!

Davide