Math Is Fun Forum

mathxyz

Member

From: Brooklyn, NY

Registered: 2024-02-24

Posts: 1,053

Graph Transformation

Plot (-4, -2) and connect with a straight line to point (-2, -2).

Afterward, connect (-2, -2) with a straight line to point (2, 2).

Finally, connect (2, 2) with a straight line to point (4, -2).

After connecting all the points as instructed, the graph of a function will appear on the xy-plane. Use the graph of f as the first step toward graphing each of the following functions:

A. h(x) = f(2x)

B. g(x) = f(-x)

mathxyz

Member

From: Brooklyn, NY

Registered: 2024-02-24

Posts: 1,053

Re: Graph Transformation

Bob,

Can you graph this function for me using software? I will then proceed to answer each question using the graph. I promise not to post so many daily questions. I certainly understand that you have a life outside of the internet.

Bob

Administrator

Registered: 2010-06-20

Posts: 10,637

Re: Graph Transformation

Again refer to the graph on a previous thread.

To get h(x) 2x inside the bracket is the same as squeezing the points closer to the y axis by a factor 1/2. The y coordinates stay the same.

eg (-4,-2) moves to (-2,-2)

g(x) reflects the points in the y axis so (-4,-2) becomes (+4,-2)

Comment on the number of posts.

I don't mind lots of posts if it means I'm helping you.  But it does get hard to keep track when so many appear at once.

Two suggestions that would help me:

Either (1) number your posts in the title so I can keep track of which ones I've viewed and dealt with,

Or (2) post the next query in the same thread you are already using so we get a chain of items all in one longer thread.  I did it that way some years back for an English lady who was studying for GCSE (late entrant). Her thread got to thousands of individual posts but it was easy for both of us to keep track.

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

mathxyz

Member

From: Brooklyn, NY

Registered: 2024-02-24

Posts: 1,053

Re: Graph Transformation

Again refer to the graph on a previous thread.

To get h(x) 2x inside the bracket is the same as squeezing the points closer to the y axis by a factor 1/2. The y coordinates stay the same.

eg (-4,-2) moves to (-2,-2)

g(x) reflects the points in the y axis so (-4,-2) becomes (+4,-2)

Comment on the number of posts.

I don't mind lots of posts if it means I'm helping you.  But it does get hard to keep track when so many appear at once.

Two suggestions that would help me:

Either (1) number your posts in the title so I can keep track of which ones I've viewed and dealt with,

Or (2) post the next query in the same thread you are already using so we get a chain of items all in one longer thread.  I did it that way some years back for an English lady who was studying for GCSE (late entrant). Her thread got to thousands of individual posts but it was easy for both of us to keep track.

Bob

To graph h(x) = f(2x), I must multiply each x-coordinate of the original function by 1/a where a is the coefficient of x in the argument for f(2x).

Yes?

To graph g(x) = f(-x), I must reflect each point of the original function about the y-axis.

You say?

Bob

Administrator

Registered: 2010-06-20

Posts: 10,637

Re: Graph Transformation

Yes to both.

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

mathxyz

Member

From: Brooklyn, NY

Registered: 2024-02-24

Posts: 1,053

Re: Graph Transformation

Yes to both.

Bob

Very cool. Interesting questions for sure. I don't recall solving questions like the ones here back in my college days.