A new chaotic map has been developed that combines the tent and logistic maps, offering more flexibility for different applications. This map can produce a range of responses by adjusting its parameters, including non-polynomial functions with fractional powers. By analyzing the map mathematically, researchers have identified a transition region where the map shifts from tent-like to logistic-like behavior. The map's properties, such as its graph, bifurcation diagram, and Lyapunov exponent, have been studied to understand its behavior. Further investigations have shown that the map can be used for image encryption, creating more secure encryption keys with improved sensitivity and cryptographic properties.