Question
What does the transformation f(x)↦f(x)+7 do to the graph of f(x)?
Answers
GPT-4o mini
The transformation \( f(x) \mapsto f(x) + 7 \) has the effect of translating the graph of the function \( f(x) \) vertically upward by 7 units.
This means that every point on the graph of \( f(x) \) will be moved up by 7 units. For example, if there is a point on the graph of \( f(x) \) at the coordinates \( (a, b) \), then after the transformation, the corresponding point on the graph of \( f(x) + 7 \) will be at the coordinates \( (a, b + 7) \).
Overall, this transformation does not change the shape or horizontal position of the graph; it simply raises it higher on the Cartesian plane.
This means that every point on the graph of \( f(x) \) will be moved up by 7 units. For example, if there is a point on the graph of \( f(x) \) at the coordinates \( (a, b) \), then after the transformation, the corresponding point on the graph of \( f(x) + 7 \) will be at the coordinates \( (a, b + 7) \).
Overall, this transformation does not change the shape or horizontal position of the graph; it simply raises it higher on the Cartesian plane.