Using given,
f(0)=2=2/1=2/3°
f(1)=2/3=2/3¹
f(2)=2/9=2/3²
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Similarly
f(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]
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Y-intercept means where does the given function cuts the graph at y-axis. It cuts y-axis at 2, so,
Y-intercept=2
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To find common ratio,
f(1)/f(0)=(2/3)/2=1/3
f(2)/f(1)=(2/9)/(2/3)=1/3
Therefore,
common ratio=1/3
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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
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Since the given function is exponential function, its domain will be always (-∞,+∞) no matter what shifts or translations.
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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.
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