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What does the transformation f(x)↦f17x do to the graph of f(x)?stretches it horizontallyshrinks it horizontallyshrinks it verticallystretches it verticallySubmit
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GPT-5 mini
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There’s an ambiguity in "f17x." Interpretations and results:
- If you mean f(17x): this is a horizontal shrink (by a factor of 1/17). Replacing x by 17x compresses the graph horizontally.
- If you mean f((1/7)x): this is a horizontal stretch (by a factor of 7). Replacing x by (1/7)x stretches the graph horizontally.
- (For completeness) If you meant 17·f(x): that would be a vertical stretch by factor 17.
Rule to remember: f(bx) compresses horizontally by 1/|b| (shrinks if |b|>1); f(x/b) stretches horizontally by |b|. Multiplying outside (a·f(x)) scales vertically.
- If you mean f(17x): this is a horizontal shrink (by a factor of 1/17). Replacing x by 17x compresses the graph horizontally.
- If you mean f((1/7)x): this is a horizontal stretch (by a factor of 7). Replacing x by (1/7)x stretches the graph horizontally.
- (For completeness) If you meant 17·f(x): that would be a vertical stretch by factor 17.
Rule to remember: f(bx) compresses horizontally by 1/|b| (shrinks if |b|>1); f(x/b) stretches horizontally by |b|. Multiplying outside (a·f(x)) scales vertically.
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