Exponential Function with Constant Term: Equation and Graph Explained #3305087 (License: Personal Use)

This diagram illustrates the general form of an exponential function with a vertical shift: y = aˣ + b, where 'a' is the base (a > 0, a ≠ 1), 'x' is the exponent, and 'b' is the constant term that shifts the curve up or down. The graph shows a classic exponential growth curve passing through the y-intercept at x = 0, where y = 1 + b, assuming a⁰ = 1. Dashed annotations clarify each component’s role in shaping the function’s behavior.

Used in educational math resources-especially algebra and precalculus-to teach transformations of exponential functions; supports learners visualizing how adding a constant alters the graph’s position without affecting its exponential nature.