Question

Select the correct statements for the exponential function $f\left(x\right)=a^x;0<a<1.$

• A. Domain $x\in R$
• B. Range $f\left(x\right)\in R$
• C. $f\left(x\right)\to \infty \text{as}x\to -\infty$
• D. Range $f\left(x\right)\in (-\infty ,0)$

Answer 1

Answer: (A), (C)

$f\left(x\right)\to \infty \text{as}x\to -\infty$

Given the exponential function $f\left(x\right)=a^x;0<a<1$
Now, we can have the graph drawn for this function as:

Now, from the graph, it's can be conclued that
Domain $x\in R$
Range $f\left(x\right)\in (0,\infty )$
Also, as $x\to -\infty ,f\left(x\right)\to \infty$