Remember to show work and explain.12) Write the equation for the function. (Find y-intercept and common ration)​f(x) = Domain:Range:

Using given,f(0)=2=2/1=2/3°f(1)=2/3=2/3¹f(2)=2/9=2/3²...........................Similarlyf(x)=2/(3^x)[Explanation: All I did here is find a pattern or behaviour of function with the help of given values of function (for x=0,1,2). You can clearly see that numerator in f(0),f(1) and f(2) remains constant while denominator follows the pattern 3ⁿ . So given function has to be equal to 2/3ⁿ]----------------------------------------------------------------------------Y-intercept means where does the given function cuts the graph at y-axis. It cuts y-axis at 2, so,Y-intercept=2----------------------------------------------------------------------------To find common ratio,f(1)/f(0)=(2/3)/2=1/3f(2)/f(1)=(2/9)/(2/3)=1/3Therefore,common ratio=1/3----------------------------------------------------------------------------The equation for function will be same as function but f(x) will be replaced by y,y=2/(3^x)➡️is the required equation----------------------------------------------------------------------------Since the given function is exponential function, its domain will be always (-∞,+∞) no matter what shifts or translations.----------------------------------------------------------------------------The graph seems to touch x-axis or the line y=0 but never reach or touch y=0 .So it doesn't quite reach y=0. Also the graph goes upward in positive direction which means it will increase infinitely in upward or positive direction. So its range will be (0,+∞) which means it will not touch y=0 line and will infinitely increase in positive or upward direction.----------------------------------------------------------------------------