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).

5 answers

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 \( k \).

Write it so i can drag it

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!

Whats the anwser

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!