this is the graph of an exponential function. write an equation for the function in the form f(x) = a(b)^x…

this is the graph of an exponential function. write an equation for the function in the form f(x) = a(b)^x. use whole numbers, decimals, or simplified fractions for the values of a and b. f(x) =

this is the graph of an exponential function. write an equation for the function in the form f(x) = a(b)^x. use whole numbers, decimals, or simplified fractions for the values of a and b. f(x) =

Answer

Explanation:

Step1: Find the y - intercept

The y - intercept is the value of the function when (x = 0). From the graph, when (x=0), (y=-4). Substituting (x = 0) into (f(x)=a(b)^{x}), we get (f(0)=a(b)^{0}=a). So (a=-4).

Step2: Find the value of (b)

Let's take another point on the graph, say ((- 1,-2)). Since (a=-4), the function is (f(x)=-4(b)^{x}). Substitute (x=-1) and (y = - 2) into the function: (-2=-4(b)^{-1}). We can rewrite the equation as (-2=\frac{-4}{b}). Cross - multiply to get (-2b=-4), then solve for (b): (b = 2).

Answer:

(f(x)=-4(2)^{x})