Math Is Fun Forum

mathxyz

Member

From: Brooklyn, NY

Registered: 2024-02-24

Posts: 1,053

Find Point For Three Graphs

In Section 3.5 in my College Algebra textbook, I came across a very interesting question with three parts. My work is wrong. My answers are incorrect. However, I will show my work and reveal the correct point answer for each part at the end of my computation.

Suppose (-3, 5) is a point on the graph of y = g(x).

A. What point is on the graph of y = g(x + 1) - 3?

B. What point is on the graph of y = -3g(x - 4) + 3?

C. What point is on the graph of y = g(3x + 9)?

For A:

Let y = g(x) = 5

y = g(x + 1) - 3

5 = g(-3 + 1) - 3

5 = g(-2) - 3

5 + 3 = g(-2)

8 = g(-2)....This leads to the point (-2, 8).

The textbook answer is (-4, 2).

How do I compute the correct point?

For B:

Let y = g(x) = 5

y = -3g(x - 4) + 3

g(x) = -3g(-3 - 4) + 3

5 = -3g(-7) + 3

5 - 3 = -3g(-7)

2 = -3g(-7)

-2/3 = g(-7)....This leads to the point (-7, -2/3).

The textbook answer is (1, -12)?

How do I compute the correct point?

For C:

Let y = g(x) = 5

y = g(3x + 9)

g(x) = g(3(-3) + 9)

5 = g(0)....This leads to the point (0, 5).

The textbook answer is (-4, 5).

How do I compute the correct point?

Bob

Administrator

Registered: 2010-06-20

Posts: 10,637

Re: Find Point For Three Graphs

A. (x+1) inside the function bracket will move the graph one place left.  The -3 outside the bracket moves the point down 3.

B. (x-4) moves the point 4 places right. That gives you g(1-4) which evaluates to 5. The times by -3 and add 3 to get the new y coordinate.

C. I know g(-3) so I put 3x+9 = -3  => 3x = -12 => x = -4.  So we then have g(3.(-4)+9) = g(-12+9) = g(-3) = 5. The y cordinate remains at 5.

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: Find Point For Three Graphs

A. (x+1) inside the function bracket will move the graph one place left.  The -3 outside the bracket moves the point down 3.

B. (x-4) moves the point 4 places right. That gives you g(1-4) which evaluates to 5. The times by -3 and add 3 to get the new y coordinate.

C. I know g(-3) so I put 3x+9 = -3  => 3x = -12 => x = -4.  So we then have g(3.(-4)+9) = g(-12+9) = g(-3) = 5. The y cordinate remains at 5.

Bob

Thank you for correcting my work.