Question
Explain how each graph is obtained from the graph of \( y=f(x) \). (a) \( y=f(x)+4 \) Stretch the graph horizontally and vertically by a factor of 4 . Shift the graph 4 units upward. Shift the graph 4 units to the right. Shift the graph 4 units downward. Shift the graph 4 units to the left.
Ask by Mccarthy Stuart. in the United States
Feb 10,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
Shift the graph 4 units upward.
Solution
The transformation y = f(x) + 4 is obtained by shifting the graph of y = f(x) vertically upward by 4 units. This is because adding 4 to the function output increases every y-value by 4, moving the entire graph up by 4 units.
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Simplify this solution Bonus Knowledge
To obtain the graph of \( y = f(x) + 4 \), you simply shift the entire graph of \( y = f(x) \) upwards by 4 units. Imagine lifting the graph up like it’s on a string! Every point on the graph moves up 4 spaces while maintaining its horizontal position. For the transformation of the graph of \( y = f(x) \), it’s essential to remember that adding a constant to the function affects its vertical position. This means that regardless of the base shape of \( f(x) \), the new graph will have all its features—like peaks and valleys—shifted up, creating a pleasing, elevated version of the original graph.
