Answer:
f(x) = 5^x -2
Explanation:
You want the equation for the graph attached.
Exponential function
The graph has a horizontal asymptote for negative values of x, and rises rapidly for positive values of x. This suggests an exponential function.
Translation
The graph of the parent exponential function will pass through the point (0, 1), which is 1 unit above the horizontal asymptote. Here, the horizontal asymptote is y = -2, and the graph passes through (0, -1).
This tells us the graph is vertically translated down 2 units and not translated horizontally at all. (Horizontal translation is equivalent to a vertical scale factor. The lack of it tells us the vertical scaling is 1.)
Base
The parent exponential function b^x rises b units above the horizontal asymptote when the value of x is 1. Here, the function rises to +3 from the asymptote of -2 at x=1, so the base of the exponential is 3-(-2) = 5.
Equation
The equation for the graph is ...
f(x) = 5^x -2
Confirmation is shown in the attachment.
#95141404393