Question
What is the direction of the vertical shift of the graph when the equation changes from f(x)=−|x| to f(x)=−|x|+4?
Answers
GPT-4o mini
The equation changes from \( f(x) = -|x| \) to \( f(x) = -|x| + 4 \).
In the function \( f(x) = -|x| \), the graph is a V-shape that opens downwards, with its vertex at the origin (0, 0).
When the equation changes to \( f(x) = -|x| + 4 \), the entire graph is shifted vertically. Specifically, the "+4" indicates a vertical shift upwards by 4 units.
To summarize, the direction of the vertical shift of the graph is **upward**.
In the function \( f(x) = -|x| \), the graph is a V-shape that opens downwards, with its vertex at the origin (0, 0).
When the equation changes to \( f(x) = -|x| + 4 \), the entire graph is shifted vertically. Specifically, the "+4" indicates a vertical shift upwards by 4 units.
To summarize, the direction of the vertical shift of the graph is **upward**.