Question

Please help this assignment is due in few hours and I am stuck on this question

Find an equation for the graph sketched below:

Answer 1

Explanation:

This graph is an upside down exponential graph moved up one unit. The growth factor is 3; therefore, the equation for this graph is

`f(x)=-(3)^x+1`

Answer 2

f(x) = -(3^x) +3

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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