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The graph if f is translated a whole number of units horizontally and vertically to obtain the graph of h The function f is def...Question
The graph of f is translated a whole number of units horizontally and vertically to obtain the graph of g
The function f is defined by f(x) = -|x|.
Write down the expression for g(x).
The function f is defined by f(x) = -|x|.
Write down the expression for g(x).
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Answer
Write it so i can drag it
Answer
Whats the anwser
Answered by
GPT-4o mini
To find the expression for the function \( g(x) \) based on the translation of the function \( f(x) = -|x| \), we need to understand how horizontal and vertical translations work.
1. **Horizontal Translation:** If you translate the graph horizontally by \( h \) units (to the right if \( h > 0 \) and to the left if \( h < 0 \)), the function changes as follows:
\[
f(x) \rightarrow f(x - h)
\]
2. **Vertical Translation:** If you translate the graph vertically by \( k \) units (upward if \( k > 0 \) and downward if \( k < 0 \)), the function changes as follows:
\[
f(x) \rightarrow f(x) + k
\]
So, to find \( g(x) \) after applying both a horizontal translation by \( h \) units and a vertical translation by \( k \) units, we would use the following expression:
\[
g(x) = f(x - h) + k
\]
Substituting \( f(x) = -|x| \) into this expression gives:
\[
g(x) = -|x - h| + k
\]
Thus, the expression for \( g(x) \) after the given translations will be:
\[
g(x) = -|x - h| + k
\]
To finalize, you would specify the values for \( h \) and \( k \) based on the specific translations performed. If values are not given, your expression should remain in terms of \( h \) and \( k \).
1. **Horizontal Translation:** If you translate the graph horizontally by \( h \) units (to the right if \( h > 0 \) and to the left if \( h < 0 \)), the function changes as follows:
\[
f(x) \rightarrow f(x - h)
\]
2. **Vertical Translation:** If you translate the graph vertically by \( k \) units (upward if \( k > 0 \) and downward if \( k < 0 \)), the function changes as follows:
\[
f(x) \rightarrow f(x) + k
\]
So, to find \( g(x) \) after applying both a horizontal translation by \( h \) units and a vertical translation by \( k \) units, we would use the following expression:
\[
g(x) = f(x - h) + k
\]
Substituting \( f(x) = -|x| \) into this expression gives:
\[
g(x) = -|x - h| + k
\]
Thus, the expression for \( g(x) \) after the given translations will be:
\[
g(x) = -|x - h| + k
\]
To finalize, you would specify the values for \( h \) and \( k \) based on the specific translations performed. If values are not given, your expression should remain in terms of \( h \) and \( k \).
Answered by
GPT-4o mini
Certainly! Here’s the expression for \( g(x) \) in a draggable format:
\[
g(x) = -|x - h| + k
\]
You can adjust \( h \) and \( k \) according to the specific translations you want to apply. Let me know if you need further assistance!
\[
g(x) = -|x - h| + k
\]
You can adjust \( h \) and \( k \) according to the specific translations you want to apply. Let me know if you need further assistance!
Answered by
GPT-4o mini
The expression for \( g(x) \) after translating the function \( f(x) = -|x| \) horizontally by \( h \) units and vertically by \( k \) units is:
\[
g(x) = -|x - h| + k
\]
If you have specific values for \( h \) (horizontal translation) and \( k \) (vertical translation), please provide those, and I can give you a more specific expression for \( g(x) \). If no specific translations are provided, \( g(x) \) simply remains in this general form.
If you are looking for a specific translation (like a certain number of units left, right, up, or down), please let me know!
\[
g(x) = -|x - h| + k
\]
If you have specific values for \( h \) (horizontal translation) and \( k \) (vertical translation), please provide those, and I can give you a more specific expression for \( g(x) \). If no specific translations are provided, \( g(x) \) simply remains in this general form.
If you are looking for a specific translation (like a certain number of units left, right, up, or down), please let me know!
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