Question

PLEASE HELP! MUST GRADUATE!

Simplify f(x) =(3x^2-4x+1)/(3x-1) . Using complete sentences, explain why f(1) = 0, f(0) = -1, and f(-1) = -2, yet f() is undefined. Make sure to show your work.

Answer 1

f(1/3) on the last one.

Answer 2

MUST GRADUATE! <3

Answer 3

factor the numerator

(3x-1)(x-1)

\[\frac{(3x-1)(x-1)}{(3x -1)}\]

cancel the common factor of (3x -1)

leaving (x -1)

now using the simplified version (x -1)

f(1) look at the factor (x -1) substituting x = 1 give 1 -1 = 0

next f(0) same process x = 0 gives 0 - 1 = -1

f(-1) same process x = -1 then -1 -1 = -2


the denominator of the fraction is (3x -1)

then you need to solve 3x -1 = 0

x = 1/3

when x = 1/3 the denominator will have a value of zero which is undefined

Answer 4

Good explanation, bro.
The most important concept here is that you can't divide by 0. So if you plug in some x and get
\[\frac{anything}{0}\]
Then there's no answer and the y value for that x is undefined.