We are asked to write a function to represent the following graph.
Notice that this is a graph of an exponential function. Therefore, it needs to be in the following form.
f(x) = a * b^xIn this form a represents the y-intercept. As we can see from the graph, our y-intercept is -2. Therefore, the value of a is -2.
f(x) = - 2 * b^x
If we examine the given options we can see that all b values are 3. By knowing this we will examine the remaining two options G and I by checking for an arbitrary point. Let's randomly choose x= - 4 and then substitute into these options to see the corresponding outputs. Let's begin with option I.
Great! We get approximately 0 for the value of f(-4). We can conclude that our exponent needs to be positive x.
f(x) = - 2 * 3^x
Therefore, our answer is option G.
