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: $f (x) \to f (x - h)$
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: $f (x) \to f (x) + k$

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!