Question

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?

Answer 1

what is the value of h?

Answer 2

I am not inderstanding what the value of h is

Answer 3

so the value of h is -2?

Answer 4

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 5

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 6

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.

1. **Original x-coordinate**: \( 5 \)
2. **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 \( 3 \)):

\[
f(5) = 3
\]

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:

\[
5 + h = 3
\]

4. 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 7

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, \( h = -2\).