\( \begin{array}{ll}\text { (1) } f(x)=-x^{3}+x^{2} & \text { (4) } f(x)=\tan (2 x) \\ \text { (2) } f(x)=-2 \cos (x)+2 & \text { (5) } f(x)=e^{x} \\ \text { (3) } f(x)=-\sqrt{5 x} & \text { (6) } f(x)=\sqrt{x}\end{array} \)

Did you know that the study of functions has deep historical roots dating back to ancient civilizations? The concept of functions began taking shape with the work of mathematicians like Euclid and later was formalized in the 17th century by thinkers such as Descartes and Leibniz. This evolution has led us to the diverse functions we explore today, from polynomials to transcendental functions! In the real world, functions are everywhere! For instance, the exponential function \( f(x)=e^{x} \) models population growth and radioactive decay, while trigonometric functions like \( f(x)=\tan(2x) \) are vital for understanding phenomena such as sound waves and light patterns. These mathematical constructs help us interpret and manage complex systems in fields as diverse as biology, engineering, and economics!