Exponential Functions
This page introduces exponential functions and their properties, essential for Edexcel year 1 maths exponential functions worksheets.
Exponential functions are defined as fx = aˣ, where a is a constant. These functions have unique properties:
Highlight: All exponential functions cross the y-axis at y = 1, as any number to the power of 0 is 1.
The page also covers differentiation of exponential functions:
Example: If fx = eˣ, then f'x = eˣ
If fx = e^kx, then f'x = ke^kx
Transformations of exponential functions are explored, including vertical and horizontal shifts, reflections, and stretches. Several examples are provided to illustrate these concepts:
Example: y = 10eˣ verticalstretch
y = 3 + 4e^2x combinationoftransformations
The page concludes with a comparison of exponential functions and their reciprocals, such as y = 2ˣ and y = 1/2ˣ, which are reflections of each other in the y-axis.