Answer:
f(x) = -(3^x) +3
Step-by-step explanation:
You want an equation for the curve shown in the graph.
Exponential function
A function that has a horizontal asymptote and rapidly changes is often an exponential function.
The location of the horizontal asymptote tells you the vertical translation. Here, the function is translated upward 3 units.
The direction of the rapid change tells you the sign of the leading coefficient. Here, it is negative.
The location of the point 1 unit different from the horizontal asymptote tells you the horizontal translation. Here, the x-value of (0, 2) is 0, so there is no horizontal translation.
The point 1 horizontal unit away from the point just found tells you the base of the exponent. Here, the point (1, 0) is 3 units different from the horizontal asymptote, so the base of the exponent is 3.
Putting these values together, we have ...
f(x) = -(3^x) +3
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Additional comment
The attached graph confirms this equation.
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