Question

Find the graph of the function $f\left(x\right)=a^x$ where $0<a<1.$

• A.
• B.
• C.
• D.

Answer 1

The correct option is B

Here, $f\left(x\right)=a^x$ and $0<a<1$

The first thing to see here is that since $a>0$ whatever x we take $a^x$ will always be greater than 0.
Let us see with an example what happens to the $f\left(x\right)$ as $x$ increases

For $a=0.5$

$(0.5{)}^1=0.5$

$(0.5{)}^2=0.25$

$(0.5{)}^3=0.125$

So, the values of $f\left(x\right)$ are decreasing as $x$ is increasing. The same trend follows for any a between 0 and 1.

So we observe that B is the correct option.