Math Is Fun Forum

nycguitarguy

Member

Registered: 2024-02-24

Posts: 542

Find x-intercepts of Two Graphs

Suppose that the x-intercepts of the graph y = f(x) are -8 and 1.

A. What are the x-intercepts of the graph of y = 2•f(x)?

B. What are the x-intercepts of the graph of y = f(-x)?

Last edited by nycguitarguy (2024-04-15 10:45:39)

nycguitarguy

Member

Registered: 2024-02-24

Posts: 542

Re: Find x-intercepts of Two Graphs

For A.

Multiply each x-coordinate of y = f(x) by 1/a.

Let a = 2

1/2 • (-8) = -4

1/2 • (1) = 1/2

You say?

For B.

Let y = f(-x)

So, -(-8) = 8

And

-(1) = -1

You say?

Bob

Administrator

Registered: 2010-06-20

Posts: 10,196

Re: Find x-intercepts of Two Graphs

I think that's ok. Is part of the question missing?

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

nycguitarguy

Member

Registered: 2024-02-24

Posts: 542

Re: Find x-intercepts of Two Graphs

I think that's ok. Is part of the question missing?

Bob

Hi Bob.

Here is the entire question:

Suppose that the x-intercepts of the graph y = f(x) are -8 and 1.

A. What are the x-intercepts of the graph of y = 2•f(x)?

B. What are the x-intercepts of the graph of y = f(-x)?

Bob

Administrator

Registered: 2010-06-20

Posts: 10,196

Re: Find x-intercepts of Two Graphs

Oh I see what happened. I read post 2 not noticing post 1.

Part B correct not A. It's to do with where the 2 is . Inside the bracket, ok. Outside it doubles the y coordinate and does nothing to the x.

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

nycguitarguy

Member

Registered: 2024-02-24

Posts: 542

Re: Find x-intercepts of Two Graphs

Oh I see what happened. I read post 2 not noticing post 1.

Part B correct not A. It's to do with where the 2 is . Inside the bracket, ok. Outside it doubles the y coordinate and does nothing to the x.

Bob

Let me try again.

Part A

We are told the x-intercepts for the original function y = f(x) are -8 and 1 which can be written as (-8, 0) and (1, 0).

We are also told that  y = 2f(x). Since 2 > 0, I multiply each y-coordinate by 2.

So, (-8, 2(0)) and (1, 2(0)) = (-8, 0) and (1, 0).

The x-intercepts of y = 2f(x) are the same as those for the original function y = f(x).

Part B

Set the argument for y = f(-x) to each given x-intercept for the original function and solve for x.

-x = -8

x = -8/-1

x = 8

-x = 1

x = 1/-1

x = -1

The x-intercepts for the graph of y = f(-x) are (8,0) and (-1,0).

You say?

Last edited by nycguitarguy (2024-04-17 09:08:17)

Bob

Administrator

Registered: 2010-06-20

Posts: 10,196

Re: Find x-intercepts of Two Graphs

Both now correct, well done.

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

nycguitarguy

Member

Registered: 2024-02-24

Posts: 542

Re: Find x-intercepts of Two Graphs

Both now correct, well done.

Bob

Very cool.