Question
(b) \( y=f(x+4) \) Shift the graph 4 units to the right. Shift the graph 4 units upward. shift the graph 4 units downward. Shift the graph 4 units to the left. stretch the graph horizontally and vertically by a factor of 4 .
Ask by Zimmerman Hamilton. in the United States
Feb 10,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
Shift the graph 4 units to the left.
Solution
To understand the transformation, note that in the function y = f(x + 4), the input to f is increased by 4. However, adding a constant inside the function argument results in a horizontal shift in the opposite direction. Therefore, the graph of y = f(x + 4) is shifted 4 units to the left.
Answer: Shift the graph 4 units to the left.
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Simplify this solution The Deep Dive
When you see \( y = f(x+4) \), this equation indicates a horizontal shift of the graph to the left by 4 units. In function transformations, adding a constant inside the function argument shifts the graph in the opposite direction. So, instead of moving right, the graph heads left! A common mistake here is to confuse horizontal shifts with vertical ones. Remember, when you shift to the left or right, it involves the \(x\) value inside the function \(f\). For vertical shifts, you would directly add or subtract from \(f(x)\) itself. Keep these straight to ace those graph transformations!
