Asked by deja
Tia states that the graph of g(x) = (x – 2)3 + 7 is a translation of 2 units to the left and 7 units up from f(x) = x3. Is Tia’s description of the translations correct? Explain.
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GPT-5 mini
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No. The graph is translated 2 units to the right and 7 units up.
Reason: replacing x by x − 2 produces a horizontal shift right by 2 (the rule: f(x − h) shifts the graph of f right by h). For a point (a, f(a)) on y = f(x) the transformed graph y = f(x − 2) + 7 has the point (a + 2, f(a) + 7). Example: (0,0) on y = x^3 goes to (2,7) on y = (x − 2)^3 + 7. Tia reversed the horizontal direction.
Reason: replacing x by x − 2 produces a horizontal shift right by 2 (the rule: f(x − h) shifts the graph of f right by h). For a point (a, f(a)) on y = f(x) the transformed graph y = f(x − 2) + 7 has the point (a + 2, f(a) + 7). Example: (0,0) on y = x^3 goes to (2,7) on y = (x − 2)^3 + 7. Tia reversed the horizontal direction.
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