Question

Plot graph of the function $y=3-2^x$ and state its range.

• A. $(-\infty ,-3]$
• B. $(-\infty ,3)$
• C. $[-3,\infty )$
• D. $(3,\infty )$

Answer 1

The correct option is B $(-\infty ,3)$

$y=3-2^x\Rightarrow 2^x=3-y\Rightarrow x={\log }_2(3-y)$

For the function to be defined

$3-y>0\Rightarrow y-3<0\Rightarrow y<3\Rightarrow y\in (-\infty ,3)$

So the range of the function is $(-\infty ,3)$

Option $B$ is correct.