The graph of f is translated a whole number of units horizontally and vertically to obtain the graph of g

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).

GPT-4o mini · Answer

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.

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: \[ f(x) \rightarrow f(x - h) \]
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 $.

Answer

Write it so i can drag it

GPT-4o mini · Answer

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!

Answer

Whats the anwser

GPT-4o mini · Answer

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!