Question

Which function is represented by the graph below? graph begins in the second quadrant near the x−axis and increases slowly while crossing the ordered pair 3, 1. Then the graph begins to increase quickly throughout the graph

Answer 1

This seems an exponential function.

Once you state that the function is exponential you can write is this form:

f(x) = A * b^x.

Then you need the y-intercept (i.e. x = 0) to find A

f(0) = A * b^0 = A

Once you have A, you can use the ordered pair (3,1) to find b

f(1) = A*b^2 = A*b = 3 => b = 3/A.

With that procedure you can find the function that represents the given graph.

Suppse the y-intercep is 0.1

Then f(0) = A = 0.1

And b = 3 / A = 3/0.1 = 30

And the function is f(x) = 0.1* 30^x