# Exponential Functions

- Author:
- gbattaly

- Topic:
- Functions

**Exponential Functions: y = a(b^x)**Prof. Battaly, College Algebra, WCC The blue curve shown on the graph has the equation y = a b^x. For this equation the variable x is in the exponent. The base, b > 0 and b ≠ 1 The sliders represent values for the coefficient a and the base b. What happens to the curve when you move the sliders (change the values of a and b)?

1. If a is positive, then y is ______________________
Why does this make sense? _______________________________
2. If a is negative, then y is _______________________
3. Can y ever be 0? ______
4. Can x ever be 0? ______
5. When a is positive and b > 1, the curve is ____________________________
When a is positive and 0 < b < 1, the curve is ____________________________
6. When a is positive, the Range is ______________________________
When a is negative, the Range is ______________________________
Gertrude Battaly, 27 March 2013, Created with GeoGebra