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=-2). Substituting (x = 0) into (y=a(b)^{x}), we get (y=a(b)^{0}=a). So (a=-2).

Step2: Find the value of (b)

Let's use another point on the graph. For example, when (x = 1), (y=-1). Substitute (a=-2), (x = 1) and (y=-1) into (y=a(b)^{x}), we have (-1=-2(b)^{1}). Solving for (b), we divide both sides of the equation by (- 2), so (b=\frac{1}{2}).

Answer:

(f(x)=-2(\frac{1}{2})^{x})