Pregunta
Iranslating the greph of a function: One step Translate each graph as specified below. (a) The graph of \( y=f(x) \) is shown. Translate it to get the graph of \( y=f(x-3) \). (b) The graph of \( y=g(x) \) is shown. Translate it to get the graph of \( y=g(x)-5 \). Part (a)
Ask by Schultz Bowers. in the United States
Feb 22,2025
Solución de inteligencia artificial de Upstudy
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To translate the graph of \( y = f(x) \) to \( y = f(x - 3) \), move every point 3 units to the right.
Solución
When you replace x with (x – 3) inside the function, every x-coordinate of the graph of y = f(x) is shifted 3 units to the right. In other words, every point (a, f(a)) on the original graph will move to (a + 3, f(a)) on the graph of y = f(x – 3). This is a horizontal translation to the right by 3 units.
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Simplifique esta solución Bonus Knowledge
When translating the graph of \( y = f(x) \) to obtain the graph of \( y = f(x - 3) \), you will shift the entire graph **3 units to the right**. This happens because the "+3" inside the function argument effectively moves the points of the graph to the right on the x-axis, making the output \( y \) values equal for inputs that are 3 units greater. Part (b) involves the graph of \( y = g(x) \). To achieve the graph of \( y = g(x) - 5 \), you simply shift the entire graph **5 units downward**. This means every point on the graph will drop by 5 units along the y-axis, maintaining the same shape but with a lower vertical position.
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