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. F(x) = f(x) + 3

B. G(x) = f(x + 2)

C. P(x) = -f(x)

How is this done?

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.

Bob

Administrator

Registered: 2010-06-20

Posts: 10,637

Re: Graph Transformation

The original is in red and F9x) in blue.

Bob

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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

https://i.imgur.com/QQNHtmb.gif

The original is in red and F9x) in blue.

Bob

Bob,

You did A for me. Thanks.

To graph G(x) = f(x + 2), I must shift each point of the original function shown in red here two units to the left.

Yes?

To graph P(x) = -f(x), I must reflect each point of the original function shown in red here about the x-axis.

Yes?

Bob

Administrator

Registered: 2010-06-20

Posts: 10,637

Re: Graph Transformation

Yes to both.

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

mathxyz

Member

From: Brooklyn, NY

Registered: 2024-02-24

Posts: 1,053

Re: Graph Transformation

Yes to both.

B

Wonderful to know I am right. Moving forward no more than 2 daily questions. Less questions means we can spend more time discussing solution steps.