Step 1 :Given two points (-2, 3/4) and (1,6), we need to find the exponential function that passes through these points. The general form of an exponential function is \(y = ab^x\).
Step 2 :We can use these points to form two equations. From the point (-2, 3/4), we get the equation \(\frac{3}{4} = ab^{-2}\). From the point (1,6), we get the equation \(6 = ab\).
Step 3 :Solving this system of equations gives three possible pairs of values for a and b. However, since we are dealing with an exponential function, we discard the solutions involving complex numbers.
Step 4 :The solution is \(a = 3\) and \(b = 2\). This gives us the exponential function \(y = 3 \cdot 2^x\).
Step 5 :\(\boxed{y = 3 \cdot 2^x}\) is the exponential function passing through the points (-2, 3/4) and (1,6).