Question

A function is defined as $f\left(x\right)=a^x\forall ϵR$ and 0 < a < 1, then which of the following is true ?
(i) It is an increasing function
(ii) It is an decreasing function
(iii) All such functions must meet at (0, 1)

• A. Only (i) is true
• B. Only (ii) is true
• C. (i) and (iii) are true
• D. (ii) and (iii) are true

Answer 1

The correct option is D (ii) and (iii) are true

$y=a^x\Rightarrow atx=0,y=1$
Hence (iii) statement is true.
at $a=\frac{1}{2},f\left(x\right)=(\frac{1}{2}{)}^x$
e.g., $a=\frac{1}{2},thenf\left(x\right)=a^x=(\frac{1}{2}{)}^x$
Hence the function is decreasing.