Math Is Fun Forum

sologuitar

Member

Registered: 2022-09-19

Posts: 467

Graph of Equations

When the graph of an equation is given, how do I find the intercepts using the graph?

How do I indicate if a given graph is symmetric with respect to the x-axis, y-axis or origin?

NOTE

I HAVE NOT UNDERSTOOD HOW TO UPLOAD PHOTOS TO THIS SITE?

Bob

Administrator

Registered: 2010-06-20

Posts: 10,640

Re: Graph of Equations

If you set x = 0 in the y = mx + c, you'll get the y intercept and y = 0 gives the x one.

Symmetry? try replacing x by -x. If the equation simplfies to the same again then the y axis is a line of symmetry.

eg. y = x^2 replace x with -x and we have y = (-x)^2 = x^2

If the replacement gives -y then the graph is rotationally symmetric aroung the origin.

eg y = x^3  replace x with -x and we have y = (-x)^3 = -x^3 = -y

You can sketch graphs where the x axis is a line of symmetry but these are not proper functions as they are not well defined.

eg. x = y^2
 
B

---

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

sologuitar

Member

Registered: 2022-09-19

Posts: 467

Re: Graph of Equations

If you set x = 0 in the y = mx + c, you'll get the y intercept and y = 0 gives the x one.

Symmetry? try replacing x by -x. If the equation simplfies to the same again then the y axis is a line of symmetry.

eg. y = x^2 replace x with -x and we have y = (-x)^2 = x^2

If the replacement gives -y then the graph is rotationally symmetric aroung the origin.

eg y = x^3  replace x with -x and we have y = (-x)^3 = -x^3 = -y

You can sketch graphs where the x axis is a line of symmetry but these are not proper functions as they are not well defined.

eg. x = y^2
 
B

I know how to do this using algebra. Can you show me using a graph?

Bob

Administrator

Registered: 2010-06-20

Posts: 10,640

Re: Graph of Equations

Plot some points, and have a look.

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

sologuitar

Member

Registered: 2022-09-19

Posts: 467

Re: Graph of Equations

Plot some points, and have a look.

Bob

Plotting points tells me where the intercepts are located. Yes? Do you have an example graph for me?

amnkb

Member

Registered: 2023-09-19

Posts: 253

Re: Graph of Equations

Plotting points tells me where the intercepts are located. Yes? Do you have an example graph for me?

make your own example (& look at the examples in the book)
like take (x - 2)(x + 3) = y
graph it & check that it crosses at x = 2, x = -3

sologuitar

Member

Registered: 2022-09-19

Posts: 467

Re: Graph of Equations

Plotting points tells me where the intercepts are located. Yes? Do you have an example graph for me?

make your own example (& look at the examples in the book)
like take (x - 2)(x + 3) = y
graph it & check that it crosses at x = 2, x = -3

Copy. Will do.