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 $\left|a\right|\&gt;1$, while compressions occur when $\left|a\right|<1$. If $a\&equals;1$, 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 $\left|b\right|\&gt;1$. If $b\&equals;1$, the graph is not affected, while if $b<0$, the graph is reflected across the $y$-axis, as well as stretched or compressed.

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

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