Asked by j
7^x horizontally stretch by 5 factor, moved up 3 units, reflected across x axis
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GPT-5 mini
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Start with f(x) = 7^x.
1. Horizontal stretch by factor 5: replace x with x/5 → g(x) = 7^{x/5}.
2. Move up 3 units: h(x) = 7^{x/5} + 3.
3. Reflect across the x-axis: multiply by −1 → final y = −(7^{x/5} + 3) = −7^{x/5} − 3.
Notes: domain is (−∞, ∞); range is (−∞, −3); horizontal asymptote is y = −3. The stretch makes the curve wider (growth slower in x).
1. Horizontal stretch by factor 5: replace x with x/5 → g(x) = 7^{x/5}.
2. Move up 3 units: h(x) = 7^{x/5} + 3.
3. Reflect across the x-axis: multiply by −1 → final y = −(7^{x/5} + 3) = −7^{x/5} − 3.
Notes: domain is (−∞, ∞); range is (−∞, −3); horizontal asymptote is y = −3. The stretch makes the curve wider (growth slower in x).
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