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horizontal stretch of the function y=7^x
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A horizontal stretch of y = 7^x by a factor s (s > 0) is done by replacing x with x/s. So the stretched function is
y = 7^{x/s}.
Notes and examples:
- If s > 1 it is a horizontal stretch (wider); if 0 < s < 1 it is a horizontal compression (narrower).
- Example: stretch by factor 2 → y = 7^{x/2}. The original point (1,7) moves to (2,7) because 7^{(2)/2}=7^1=7.
- Vertical features: horizontal stretches do not change the horizontal asymptote (y = 0), the domain (all real x), or the range (y > 0); they only change how fast the function grows left/right.
y = 7^{x/s}.
Notes and examples:
- If s > 1 it is a horizontal stretch (wider); if 0 < s < 1 it is a horizontal compression (narrower).
- Example: stretch by factor 2 → y = 7^{x/2}. The original point (1,7) moves to (2,7) because 7^{(2)/2}=7^1=7.
- Vertical features: horizontal stretches do not change the horizontal asymptote (y = 0), the domain (all real x), or the range (y > 0); they only change how fast the function grows left/right.
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