Scaling - Maple Help

Scaling

 Main Concept A graph can be horizontally or vertically scaled by multiplying each $x$ or $y$ coordinate of the graph by a constant factor. This can be represented in function form as $a\cdot f\left(x\right)$ for a vertical scaling, or $f\left(b\cdot x\right)$ for a horizontal scaling.   A graph is vertically compressed if the $y$ values for a given $x$ value become smaller. If the $y$ values become larger, the graph is vertically stretched. Vertical stretches occur when $\left|a\right|>1$, while compressions occur when $\left|a\right|<1$. If $a=1$, the graph is not affected, while if $a<0$, the graph is reflected across the $x$-axis, as well as stretched or compressed.   Similarly, a graph is horizontally compressed if the $x$ values decrease for a given $y$ value. If they increase, the graph is horizontally stretched. Horizontal scaling, like translations, are the opposite of what is expected. Stretches occur when $\left|b\right|<1$, while compressions occur when $\left|b\right|>1$. If $b=1$, the graph is not affected, while if $b<0$, the graph is reflected across the $y$-axis, as well as stretched or compressed.

Use the following demonstration to experiment with stretching and compressing functions. Choose a function from the drop down list, as well as which way you would like to scale it. Enter the factor by which you want to scale your function and click Scale.

 x^2sin(x)x^3+2*x^2-5*x-6ln(x)2^x(x^2-3*x-2)/(x^2-4)             Scale by:



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