Scaling and Reflecting of Function

==2024-11-14

Theory

For a function $y=f(x)$:

For scaling, → c>0

For reflecting, c<0.

where, c = no. for scaled function $y=c\ast f(x)$ or $y=f(c\ast x)$

For $y=c\ast f(x)$

1. If $c\in (0,1)$, The graph compresses vertically.

2. If $c\in (1,\infty )$, The graph stretches vertically.

For $y=f(c\ast x)$

1. If $c\in (0,1)$, The graph compresses horizontally.

2. If $c\in (0,1)$, The graph stretches horizontally.

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Examples

Here, $f(x)=x^2$ → blue

1. In cf(x),

   1. $c\in (0,1)$ → yellow
   2. $c\in (1,\infty )$ → red

2. In f(cx), 3. $c\in (0,1)$ → purple 4. $c\in (1,\infty )$ → black

3. reflection → c < 0 → green

f(x)=x^2|blue
f(x)=0.5*x^2|yellow
f(x)=2*x^2|red
f(x)=(0.5x)^2|purple
f(x)=(2x)^2|black
f(x)=-x^2|green

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PTR