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=2/3¹

f(2)=2/9=2/3²

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]

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=1/3

f(2)/f(1)=(2/9)/(2/3)=1/3

Therefore,

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.

f(2x−x2)=−3x2+6x−1

step-by-step explanation:

set up the composite function and evaluate.

f(2x−x2)=−3x2+6x−1