Question

When looking at the rational function f of x equals the quantity x minus one times the quantity x plus two times the quantity x plus four all divided by the quantity x plus one times the quantity x minus two times the quantity x minus four, Bella and Edward have two different thoughts. Bella says that the function is defined at x = –1, x = 2, and x = 4. Edward says that the function is undefined at those x values. Who is correct? Justify your reasoning.

Answer 1

@jim_thompson5910

Answer 2

@freckles

Answer 3

` f of x equals the quantity x minus one times the quantity x plus two times the quantity x plus four all divided by the quantity x plus one times the quantity x minus two times the quantity x minus four` what a mess...

hopefully I translated the word problem into the proper function

\[\Large f(x) = \frac{(x-1)(x+2)(x+4)}{(x+1)(x-2)(x-4)}\]

let me know if I did or not

Answer 4

yes you did

Answer 5

ok great

Answer 6

`Bella says that the function is defined at x = –1, x = 2, and x = 4`

let's check this claim. If we were to replace EVERY x with a value like x = 4, then...

\[\Large f(x) = \frac{(x-1)(x+2)(x+4)}{(x+1)(x-2)(x-4)}\]
\[\Large f(4) = \frac{(4-1)(4+2)(4+4)}{(4+1)(4-2)(4-4)}\]
\[\Large f(4) = \frac{(3)(6)(8)}{(5)(2)(0)}\]
\[\Large f(4) = \frac{144}{0}\]
\[\Large f(4) = \text{Undefined}\]

the result is undefined because we cannot divide by zero. We can't have 0 in the denominator

Answer 7

`Bella says that the function is defined at x = –1, x = 2, and x = 4`

so Bella is wrong. At least about the `x=4` part. I recommend you check `x=-1` and `x=2`

Answer 8

ok thank you

Answer 9

no problem

Answer 10

the rest are not undefined

Answer 11

correct,x=-1 and x=2 are also undefined because they make the denominator 0

Answer 12

oh wait, you should say "the rest are undefined" or "the rest are not defined"

Answer 13

i got f(-1)=-4 and f(2)= 11

Answer 14

you did something wrong

Answer 15

f(-1) = (-1 - 1)(-1 + 2)(-1 + 4)/ (-1 + 1)(-1 - 2)(-1 - 4)

= -2 + 1 + 3/ 0 - 3 - 5

= 2/-8

f(-1) = -4

Answer 16

f(2) = (2 - 1)(2 + 2)(2 + 4)/ (2 + 1)(2 - 2)(2 - 4)

= 1 + 4 + 6/ 3 + 0 - 2

= 11/1

= 11

Answer 17

are you gonna help me still? @jim_thompson5910

Answer 18

sorry my notification thing isn't working properly

Answer 19

thats ok

Answer 20

(-1 + 1)(-1 - 2)(-1 - 4) = 0*(-3)*(-5) = 0 is in the denominator

Answer 21

the parenthesis next to each other means multiply

Answer 22

make sense?

Answer 23

ohhh ok thank you so much for the help.

Answer 24

no problem