T2W1L3: transformation of functions

methods cambridge 6e - 6h

• functions are translated $y=f(x-h)$ is that y=f(x) translated right h units
• functions are translated $y=f(x)+h$ is that $y=f(x)$ translated up h units

dilations §

• functions are dilated as follows
• $y=af(x)$ is $y=f(x)$ dilated by a factor of $a$ from the x-axis (or along the y-axis)
• $y=f(bx)$ is that of $y=f(x)$ dilated by a factor of $\frac{1}{b}$ from the y-axis (or along the x-axis)

reflection §

• functions are reflected as follows:
• $y=-f(x)$ is that of $y=f(x)$ reflected about the x-axis
• $y=f(-x)$ is that of $y=f(x)$ reflected about the y-axis

the transformation of inside the function is in a way opposite the transformation outside the function.

$f(x)=\frac{1}{2x-1}+3$ $HT-4$ $f(x)\to f(x+4)$ VT + 5 $f(x+4)\to f(x+4)+5$ $g(x)=f(x+4)+5$ $=\frac{1}{2(x+4)-1}+3+5$ $=\frac{1}{2x+7}+8$

if you combine two transformations in different orders, you get different results eg dilating first vs translating first

	dilating first	translating first
vertical	f(x) dilate by $a$ from x-axis $af(x)$ translate up k units $af(x)+k$	$f(x)$ translate up $k$ units $f(x)+k$ dilate by $a$ from x-axis $a(f(x)+k)$