Question

write a rule for g that represents a translation 3 units left and 2 units up, followed by a reflection in the y -axis of the graph of $f(x)=log_{1/2}x$. $g(x)=\square$

Explanation:

Step1: Translate 3 units left

Replace $x$ with $x+3$:
$g_1(x) = \log_{1/2}(x+3)$

Step2: Translate 2 units up

Add 2 to the function:
$g_2(x) = \log_{1/2}(x+3) + 2$

Step3: Reflect over y-axis

Replace $x$ with $-x$:
$g(x) = \log_{1/2}(-x+3) + 2$

Answer:

$\log_{1/2}(-x+3) + 2$