A point is translated on the coordinate plane from (5,6) to (3,6). Peter writes the function f(x)=x+h to describe the translation. What is the value of h?

Question

GPT-4o mini · Answer

To determine the value of $ h $ in the function $ f(x) = x + h $ that describes the translation from the point $ (5, 6) $ to the point $ (3, 6) $, we need to focus on the x-coordinate. The point is translated from $ x = 5 $ to $ x = 3 $. We can express this translation in terms of the function $ f(x) $: $$ f(5) = 3 $$ Substituting $ x = 5 $ into the function, we have: $$ f(5) = 5 + h $$ Setting this equal to the new x-coordinate after the translation: $$ 5 + h = 3 $$ Now, we solve for $ h $: $$ h = 3 - 5 = -2 $$ Thus, the value of $ h $ is $$ \boxed{-2} $$

Answer

what is the value of h?

GPT-4o mini · Answer

We previously determined that the value of $ h $ in the function $ f(x) = x + h $ for the translation from the point $ (5, 6) $ to $ (3, 6) $ is:

\[ h = -2 \]

Thus, the value of $ h $ is

\[ \boxed{-2} \]

Answer

I am not inderstanding what the value of h is

GPT-4o mini · Answer

Let's break it down step by step.

You have a point at $ (5, 6) $ which is being translated (moved) to the point $ (3, 6) $. This translation involves a change in the x-coordinate from $ 5 $ to $ 3 $, while the y-coordinate remains the same ($ 6 $).

We are using a function $ f(x) = x + h $ to describe this translation. The variable $ h $ represents how much we need to adjust $ x $ in order to move from the original point to the new point.

Original x-coordinate: $ 5 $
New x-coordinate: $ 3 $

The translation can be expressed mathematically as follows:

The function should take the original $ x $ value (which is $ 5 $) and result in the new $ x $ value (which is $ 3 $):

\[ f(5) = 3 \]

From the function $ f(x) = x + h $, we plug in $ 5 $:

\[ f(5) = 5 + h \]

We set this equal to the new x-coordinate:

\[ 5 + h = 3 \]
To find the value of $ h $, we subtract $ 5 $ from both sides:

\[ h = 3 - 5 \]

\[ h = -2 \]

So, $ h $ represents the amount you need to subtract from $ 5 $ to get $ 3 $. Thus, the value of $ h $ is:

\[ \boxed{-2} \]

If you have any further questions or need additional clarification, feel free to ask!

Answer

so the value of h is -2?

GPT-4o mini · Answer

Yes, that is correct! The value of $ h $ is indeed $-2$. This means that in the function $ f(x) = x + h $, in order to translate the point from $ (5, 6) $ to $ (3, 6) $, you need to subtract $ 2 $ from the x-coordinate. So, when you set $ h = -2 $: $$ f(x) = x - 2 $$ Using $ f(5) $: $$ f(5) = 5 - 2 = 3 $$ This confirms that it translates the point correctly. Thus, $ h = -2$.