Question

Using complete sentences, explain why f(1) = 0, f(0) = -1, and f(-1) = -2, yet f(one-third) is undefined. Be sure to show your work.

Answer 1

Will fan!

Answer 2

@mathstudent55

Answer 3

Is there a function that comes with this problem or do we need to make up a function?

Answer 4

well the first part of the question is : Simplify f(x) = the quantity 3 x-squared minus 4x plus 1 all over 3x minus 1. but idk if that goes wit it

Answer 5

with*

Answer 6

@mathstudent55
@Paynesdad

Answer 7

It does go with it.

Answer 8

Oh..

Answer 9

\( f(x) = \dfrac{3x^2 -4x+1}{3x - 1} \)

L:et's find f(1):

\( f(1) = \dfrac{3(1^2) -4(1)+1}{3(1) - 1} = \dfrac{3 -4+1}{3 - 1} = \dfrac{0}{2} = 0\)

Ok?

Answer 10

okay!

Answer 11

You see that as the problem read, f(1) = 0. That make sense.

Answer 12

Yes so do I just fill in x with what ever f is ? Also how do you know if something is underfined?

Answer 13

Now let's calculate f(0)

\(f(0) = \dfrac{3(0^2) -4(0)+1}{3(0) - 1} = \dfrac{0 -0+1}{0 - 1} = \dfrac{1}{-1} = -1\)

Once again, we confirm that the given info is correct. f(0) = -1

Answer 14

Now we can calculate f(-1):

\(f(-1) = \dfrac{3(-1)^2 -4(-1)+1}{3(-1) - 1} = \dfrac{3 +4+1}{-3 - 1} = \dfrac{8}{-4} = -2\)

Once again, we have shown the given info to be true. f(-1) = -2.

Answer 15

Now comes the last step, to show that \(f \left( \dfrac{1}{3} \right) \) is undefined.
Usually in functions, you get undefined results when they involve division by zero.

Answer 16

\(f(\frac{1}{3}) = \dfrac{3(\frac{1}{3})^2 -4(\frac{1}{3})+1}{3(\frac{1}{3}) - 1} \)

Can you simplify the denominator? What do you get for the denominator?

Answer 17

.5

Answer 18

1.5

Answer 19

*

Answer 20

No.
\( 3(\dfrac{1}{3}) - 1 = ? \)
What is 3 times one-third?

Answer 21

oh thought it was 1/2 not 1/3
and its zero so i getttt ittt!!! THanks sooo much!

Answer 22

Correct. Since the denominator is zero when x = 1/3, the function is undefined
at x = 1/3.