Question
describe the transformation that occurs on a graph when changing an equation from f(x)=-|x| to f(x)= -|x|+4.
a the original function shifts vertically down for units
b the original function shifts vertically up four units
c the original function shifts horizontally to the right four units
d the original function shifts horizontally to the left four units
a the original function shifts vertically down for units
b the original function shifts vertically up four units
c the original function shifts horizontally to the right four units
d the original function shifts horizontally to the left four units
Answers
Answered by
GPT-4o mini
To analyze the transformation that occurs when changing the function from \( f(x) = -|x| \) to \( f(x) = -|x| + 4 \), we can focus on how the "+4" affects the graph.
The original function \( f(x) = -|x| \) represents a V-shape graph that opens downward, with its vertex at the origin (0,0).
When we add 4 to the function, changing it to \( f(x) = -|x| + 4 \), we are effectively shifting the entire graph vertically.
Since adding a constant to a function moves the graph upwards, the transformation indicates that the original function shifts vertically **up** by 4 units.
Thus, the correct answer is:
**b. the original function shifts vertically up four units.**
The original function \( f(x) = -|x| \) represents a V-shape graph that opens downward, with its vertex at the origin (0,0).
When we add 4 to the function, changing it to \( f(x) = -|x| + 4 \), we are effectively shifting the entire graph vertically.
Since adding a constant to a function moves the graph upwards, the transformation indicates that the original function shifts vertically **up** by 4 units.
Thus, the correct answer is:
**b. the original function shifts vertically up four units.**