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nycguitarguy

Member

Registered: 2024-02-24

Posts: 549

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 = f(x + 4)?

B. What are the x-intercepts  of the graph of y = f(x - 3)?

Bob

Administrator

Registered: 2010-06-20

Posts: 10,198

Re: Find x-intercepts of Two Graphs

If all points move 4 left then that's what happens to the intercepts.

You've posted a load more similar questions but it looks like you can do these, so I'll concentrate on the ones you have tried and got stuck on.

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: 549

Re: Find x-intercepts of Two Graphs

If all points move 4 left then that's what happens to the intercepts.

You've posted a load more similar questions but it looks like you can do these, so I'll concentrate on the ones you have tried and got stuck on.

Bob

Ok. I will work on these later and wait for your correction.

nycguitarguy

Member

Registered: 2024-02-24

Posts: 549

Re: Find x-intercepts of Two Graphs

If all points move 4 left then that's what happens to the intercepts.

You've posted a load more similar questions but it looks like you can do these, so I'll concentrate on the ones you have tried and got stuck on.

Bob

For A

y = f(x + 4)

y = f(-8 + 4)

y = f(-4)

One x-intercept is -4.

y = f(x + 4)

y = f(1 + 4)

y = f(5)

Another x-intercept is 5.

You say?

For B

y = f(x - 3)

y = f(-8 - 3)

y = f(-11)

One x-intercept is -11.

y = f(x - 3)

y = f(1 - 3)

y = f(-2)

Another x-intercept is -2.

You say?

Bob

Administrator

Registered: 2010-06-20

Posts: 10,198

Re: Find x-intercepts of Two Graphs

For f(x) we know that f(-8) = 0

For the new function we have f(x+4) . So what value of x makes this 0 again.  f(-12 + 4) = f(-8) = 0 so the intercept is at x=-12

That shows that the graph has moved 4 units left ( from -8 back to -12).

Try the other part again, please.

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: 549

Re: Find x-intercepts of Two Graphs

For f(x) we know that f(-8) = 0

For the new function we have f(x+4) . So what value of x makes this 0 again.  f(-12+4) = f(-8) = 0 so the intercept is at x=-12

That shows that the graph has moved 4 units left ( from -8 back to -12).

Try the other part again, please.

Bob

I will need to review this again. Moving forward no more than 2 questions posted on any given day.

nycguitarguy

Member

Registered: 2024-02-24

Posts: 549

Re: Find x-intercepts of Two Graphs

For f(x) we know that f(-8) = 0

For the new function we have f(x+4) . So what value of x makes this 0 again.  f(-12+4) = f(-8) = 0 so the intercept is at x=-12

That shows that the graph has moved 4 units left ( from -8 back to -12).

Try the other part again, please.

Bob

Part A

Set x + 4 = 0 and solve for x.

x + 4 = 0

x = -4

The x-intercept for y = f(x + 4) is (-4, 0).

Part B

Set x - 3 = to the given x-intercepts for the original function y = f(x).

x - 3 = -8

x = -8 + 3

x = -5

Do the same for x - 3 = 1.

x - 3 = 1

x = 1 + 3

x = 4

The x-intercepts for y = f(x - 3) are (-5, 0) and (4, 0).

You say?

Bob

Administrator

Registered: 2010-06-20

Posts: 10,198

Re: Find x-intercepts of Two Graphs

Part A

Set x + 4 = 0 and solve for x.

No. You want x + 4 = -8

Part B is correct.

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: 549

Re: Find x-intercepts of Two Graphs

Part A

Set x + 4 = 0 and solve for x.

No. You want x + 4 = -8

Part B is correct.

Bob

Part A

x + 4 = -8

x = -8 -4

x = -12

The x-intercept for y = f(x + 4) is (-12, 0).

Bob

Administrator

Registered: 2010-06-20

Posts: 10,198

Re: Find x-intercepts of Two Graphs

That's it. 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: 549

Re: Find x-intercepts of Two Graphs

That's it. Well done.

Bob

Very good.

nycguitarguy

Member

Registered: 2024-02-24

Posts: 549

Re: Find x-intercepts of Two Graphs

That's it. Well done.

Bob

One thing I have learned through the years about mathematics is the fact that I am not going to understand every chapter, every section and this is ok. I am doing a self-study of math learned back in the late 80s and early 90s. I like this website but wish we had more participants.

I thank you for taking time out to help out when possible. We can both agree, I'm sure, that math textbooks are not student friendly. Math teachers are good at solving math problems but often don't know how to explain the material well in textbooks. This is why I am a big fan of the MATH FOR DUMMIES books.

You say?