The function [tex] y=3^x [/tex] is incresing and have positive values for all x. Then the function [tex] y=\dfrac{1}{5}\cdot 3^x [/tex] is also increasing and have positive values for all x. This means that options B (values are negative) and D (function is decreasing) are incorrect.
At x=0, [tex] y=\dfrac{1}{5} \cdot 3^x=\dfrac{1}{5} \cdot 3^0=\dfrac{1}{5} \cdot 1=\dfrac{1}{5} [/tex].
In option A graph of the function passes through point (0,y), where y is near 3. In option C graph of the function passes through point (0,y), where y is near 1/5. So, you can conclude that the option C is correct.
