Math Is Fun Forum

mathland

Member

Registered: 2021-03-25

Posts: 444

Test for Symmetry

Test each equation for symmetry.

I forgot how to do this symmetry stuff. Seeking the steps.

1. y = sqrt{1 − x}

2. y = ∣x − 6∣

3. y = 1 − ∣x∣

4. x = y^2 − 5

Bob

Administrator

Registered: 2010-06-20

Posts: 10,580

Re: Test for Symmetry

hi,

Hope you are well.

You can test if the y axis is a line of symmetry by replacing x with -x.  If the equation gives the same value for y then you know that

f(x) = f(-x) and so the y axis is a line of symmetry.

For the last one do a similar thing by replacing y with - y.  For that one it'll be the x axis.

There are other, more complex symmetry considerations, eg.  y = 1/x has the line y = x as a line of symmetry, but it doesn't look like any of the ones you have posted are like this.

The second one has a line that is not the y axis.  If you cannot spot it, try making the graph.

Bob

---

Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you!  …………….Bob

mathland

Member

Registered: 2021-03-25

Posts: 444

Re: Test for Symmetry

hi,

Hope you are well.

You can test if the y axis is a line of symmetry by replacing x with -x.  If the equation gives the same value for y then you know that

f(x) = f(-x) and so the y axis is a line of symmetry.

For the last one do a similar thing by replacing y with - y.  For that one it'll be the x axis.

There are other, more complex symmetry considerations, eg.  y = 1/x has the line y = x as a line of symmetry, but it doesn't look like any of the ones you have posted are like this.

The second one has a line that is not the y axis.  If you cannot spot it, try making the graph.

Bob

I learned this symmetry stuff years ago. I will search for videos on You Tube.

Bob

Administrator

Registered: 2010-06-20

Posts: 10,580

Re: Test for Symmetry

I'm having trouble knowing how to respond to your after help posts.

I learned this symmetry stuff years ago

What does this mean?  It sounds like you are saying you didn't need any help with this.

On other occasions you post that the topic was easy.  ??? If it was easy then why post for help.  If you mean "You've made it really easy for me to understand" then please say exactly that because that will make me feel great and encourage me to help you again.

If you mean "This is easy for me", then please don't ask for help on that topic at all.  Then I can concentrate on giving help where it's really needed.

Bob

---

Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you!  …………….Bob

mathland

Member

Registered: 2021-03-25

Posts: 444

Re: Test for Symmetry

I'm having trouble knowing how to respond to your after help posts.

I learned this symmetry stuff years ago

What does this mean?  It sounds like you are saying you didn't need any help with this.

On other occasions you post that the topic was easy.  ??? If it was easy then why post for help.  If you mean "You've made it really easy for me to understand" then please say exactly that because that will make me feel great and encourage me to help you again.

If you mean "This is easy for me", then please don't ask for help on that topic at all.  Then I can concentrate on giving help where it's really needed.

Bob

By easy, I mean that learning this material years ago was easy compared to other math topics. I am currently learning Calculus 1 but occasionally I like to revisit Precalculus and select topics that I want to touch base on. Testing for symmetry is not abstract algebra or linear algebra. Can we agree here?

If the rules for testing for symmetry are explained again, I will pick up on it right away considering that I took Precalculus at Lehman College in the Spring 1993 semester and earned an A minus in the course. I took the class as an elective course not a required course. From now on, I will only post questions that throw me into a loop. I don't want to waste your time or anyone else's time with questions that are not too complicated.