Could someone please help me with this problem?

Question

Let f(x) = 5(2 – x)/(x – 3)^3. Determine the coordinates of the x and y intercepts.

a) (0, -10/27), (2, 0)
b) no x- or y-intercepts
c) (0, 3), (2, 0)
d) (3,0), (0, -10/27)

Answer 1

b) no x- or y-intercepts
since its an equation with 1 variable

Answer 2

OK, f(x) is just another way of saying "y", as long as you have a function. So to find the y-intercept,

0= 5(2-x)/(x-3)^3 multiply through by the denominator:

0 = 5(2-x) divide by 5

0 = 2-x and therefore x=2. So the y-intercept is (2,0).

You do the same for x. In this case, then,

y = 5(2-0)/(0-3)^3

or

y=10/-27

so the x-intercept if (0,-10/27)

so the answer is "a"

Answer 3

Put f(x) =0 so 2-x=0 and x=2 (x intercept)
put x= 0 and f(0)=-10/27 (y intercept) (a)