Question

I need to give an equation for an absolute value function that has a minimum. How do I determine that it has a minimum?

Answer 1

Do you know what the graph of an absolute value function looks like?

Answer 2

I know that it is the shape of a V but i dont know how to determine what the minimum or maximum is. or even how to put it into an equation for that fact.

Answer 3

what is the value at the lowest point on the graph?

Answer 4

zero?

Answer 5

right

Answer 6

The "value" refers to the y value

Answer 7

the position of the graph in y represents the "output" of the function

Answer 8

so the lowest position on the graph corresponds to the minimum

Answer 9

ok. but how do i make an equation? I have to write an equation for an absolute value function. I dont know how to do that.

Answer 10

Do you know how to write the most basic absolute value function possible?

Answer 11

that corresponds to the graph that I drew and would be a correct answer

Answer 12

\[y=\left| x \right|\]?

Answer 13

thats right

Answer 14

So long as the equation is not in the form y = -|x|, it will have a mininum

Answer 15

so the simplest case works fine

Answer 16

ok. so then for an equation with a maximum it could be anything that is \[y=+\left| x \right|\]

Answer 17

????

Answer 18

If it is positive it wont have a maximum.

Answer 19

look at the graph I drew before and observe how it increases forever in both directions

Answer 20

ok. then how do I write one with a maximum?

Answer 21

When you reflect the graph across the x axis, you can see how what was a minimum before is not a maximum instead

Answer 22

is now**

Answer 23

So y = - |x| has a maximum

Answer 24

ohhhhh. ok. Now i get it. Thank you so much for your help :) I may need it again in a little bit. :)

Answer 25

np. If you found it helpful can you award a medal please? I would appreciate it. Trying to increase my rank. :)

Answer 26

haha :) Sure can do :)

Answer 27

thanks

Answer 28

yupp :)

Answer 29

ok. so what is the point called where the maximum or minimum value occurs?

Answer 30

they're called absolute maximums or absolute minimums

Answer 31

some functions need to be examined more carefully to make sure you have found the absolute max and not just a local max

Answer 32

ok. so now i have one more more question. How do we know that absolute value functions are not one-to-one? I have no idea what this means

Answer 33

Do you understand the definition of a function?

Answer 34

apparently not. I hate math. haha

Answer 35

Okay, well a function describes a relationship between the set of numbers that can be used as input for the function, and the set of numbers that come back out as output

Answer 36

This is why the value of y is considered to be the "value" of the function at that point

Answer 37

Because if you put in x, you get back that y.

Answer 38

ok. so what does it mean when it is one-to-one? I dont understand that.

Answer 39

A function is a relationship that is slightly more special, in that each output can correspond ONLY to a single input

Answer 40

like a circle can't be a function because each position in x is related to 2 positions in y.

Answer 41

I know you think I'm not getting to your question, but I am

Answer 42

beause you have to understand this to know what one-to-one refers to

Answer 43

So in order to check if something is a function, you can look for what is called the vertical line test

Answer 44

Oh its fine. I just dont understand any of this math. and we dont have a text book for my class. so I really dont know what or how I am supposed to be doing this.

Answer 45

Since the vertical line passes through 2 points in the same x position, it can't be a function

Answer 46

In order for a function to be ONE-TO-ONE, you look for something called a horizontal line test

Answer 47

ok. i understand the horizontal line test. I just dont know why an absolute function can't be one-to-one

Answer 48

because one to one refers to a relationship such that each y value is paired with ONLY ONE x value

Answer 49

an absolute value function is such that each y is paired with 2 x's

Answer 50

so it fails the horizontal line test on that basis

Answer 51

ok. got it. :)