Big Ideas:
Exponential functions are strictly increasing if the base is greater than 1.
Exponential functions are one-to-one, and map elements of the domain to unique elements of the range.
Exponential functions are invertible.
In this task students show that exponential functions are one-to-one by first showing that exponential functions (with a growth factor greater than 1) are strictly increasing. Establishing that exponential functions are one-to-one is a key step towards showing that exponential functions are invertible. In future lessons, the logarithm is introduced as the inverse of the exponent.
Vocabulary:
exponential function, one-to-one
Lesson plan