Question

help putting equation into point slope formula

Answer 1

i subtract the x and get -y^4=-x+1 but not sure what to do after this.

Answer 2

except i suppose then i would divide by -1 and get y^4=x-1

Answer 3

how do i get the y on its own?

Answer 4

hmm what are you supposed to do again?

Answer 5

im just trying to get it into point slope formula so i need the y to be on its own but im not sure how to get it away from the 4th... since it is y^4

Answer 6

and then once i have the point slope formula i just put it in my graphing calculator to see if it passes the vertical line test.

Answer 7

graph the equation using something like this

https://www.desmos.com/calculator

and see if it passes the vertical line test

Answer 8

ah i just did, it does not pass the vertical line test. i thought i needed to put it into point slope formula first.

Answer 9

so now how do i decide between A and C?

Answer 10

Would it be C? because that answer choice is saying that the input would repeat?

Answer 11

point slope formula only applies to linear equations

this isn't linear

Answer 12

well.. what's an OUTPUT and what's an INPUT?

Answer 13

to figure out which one it is, look back at your notes as to what makes something a function

it has to do with the inputs and outputs

Answer 14

yes well i know that input cannot repeat...correct?

Answer 15

\(\large { x-y^4=1\implies x+1=y^4\qquad taking\quad \sqrt[4]{\qquad }\textit{ to both sides}
\\ \quad \\
\pm \sqrt[4]{x+1}=\sqrt[4]{y^4}\implies \pm\sqrt[4]{x+1}=y
}\)

Answer 16

check your INPUTS and see what OUTPUTS it gives

Answer 17

hmm actually.. I have to change a sign there

Answer 18

yeah if you had say x = 1 and you plugged it into this "function", you cannot have that input of x = 1 produce multiple outputs

Rule: a function has EXACTLY ONE output for any given input

Answer 19

\(\large {
x-y^4=1\implies x-1=y^4\qquad taking\quad \sqrt[4]{\qquad }\textit{ to both sides}
\\ \quad \\
\pm \sqrt[4]{x-1}=\sqrt[4]{y^4}\implies \pm\sqrt[4]{x-1}=y

}\)

Answer 20

hmm okay..so how do i test that out? how am i to check if it doesnt repeat?

Answer 21

look at the graph and look at say, x = 2

Answer 22

okay and here is the graph just for easy to view purposes hah

Answer 23

drawing a vertical line through x = 2 means it goes through the points (2,1) and (2,-1) on the graph. So this fails the vertical line test

It's not a function because the input x = 2 produces the two outputs: y = 1 and y = -1

Answer 24

if you were to plug x = 2 into the function, you should expect one output

Answer 25

ah okay i see so the output is what is repeating technically

Answer 26

looking at the option choices i still cant decide though...they sound so alike i cant quite tell what each of them mean

Answer 27

@jdoe0001 do you think it is A or C?

Answer 28

did you graph the equation?

Answer 29

yes there is a picture of it above^

Answer 30

im just having a hard time understanding the difference between each of the answer choices and why it would be either of those.

Answer 31

let see if we can reword it


A) no, at least one "x value" results in more than one "y value"

C) no, at least one "y value" results in more than one "x value"

what do you think?

Answer 32

maybe it will help if you cross out the "at least" from each answer choice

Answer 33

I would think it was C then because the x values are repeating

Answer 34

ah no wait! the y values are repeating? now that i look at the graph

Answer 35

A) one input results in more than one output

C) one output results in more than one input

Answer 36

well.. if the "x values" are repeating
that means that "more than one INPUT is resulting in the same OUTPUT"

Answer 37

I am thinking the answer is A then

Answer 38

"I am thinking the answer is A then" \(\large \checkmark\)

Answer 39

thank you both very much!

Answer 40

yw