Final Answer:
The completed guided notes show how to graph exponential functions by:
1. Identifying the base (e.g., 3, 1/4, 3/4, 6) to determine growth (base > 1) or decay (0 < base < 1).
2. Creating a table of values (e.g., for $ f(x) = 3^x $: x = −1 → y = 1/3; x = 0 → y = 1; x = 1 → y = 3).
3. Plotting points and drawing a smooth curve.
Key characteristics for each function:
- $ f(x) = 3^x $: y-intercept (0,1), asymptote y = 0, domain all real numbers, range $ y > 0 $.
- $ g(x) = \left(\frac{1}{4}\right)^x $: y-intercept (0,1), asymptote y = 0, domain all real numbers, range $ y > 0 $.
- $ d(x) = \left(\frac{3}{4}\right)^x $: same intercept/asymptote/domain/range as above (decay since base < 1).
- $ m(x) = 6^x $: y-intercept (0,1), asymptote y = 0, domain all real numbers, range $ y > 0 $.
All graphs pass through (0,1), approach y = 0 but never touch it, and are always positive.
Parent Tip: Review the logic above to help your child master the concept of algebra 2 worksheet solving exponential equations.
