(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 .
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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!
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