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nycguitarguy

Member

From: Brooklyn, NY

Registered: 2024-02-24

Posts: 566

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?

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The Rapture is the central event in biblical prophecy. The greatest truth about the Rapture is not its timing but it's reality. The Rapture will be the great disappearance.

Dr. David Jeremiah

Bob

Administrator

Registered: 2010-06-20

Posts: 10,212

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

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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

nycguitarguy

Member

From: Brooklyn, NY

Registered: 2024-02-24

Posts: 566

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.

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The Rapture is the central event in biblical prophecy. The greatest truth about the Rapture is not its timing but it's reality. The Rapture will be the great disappearance.

Dr. David Jeremiah