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

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