Exponential Functions

Hi everyone, this is Austin Granados from Mr.P's Pre-cal 40s section C class. Today we learned about exponential functions. I put (exp) or (neg.exp) to show that it is an exponent of X or M.

f(x)=a(exp)x where a and b are real numbers, so that a cannot equal 0, where b > 0, and b cannot equal 1.

a is a constant

b is a base

x is an exponent

Basic Curve: f(x)=a(exp)x where a > 1.

y=a(neg. exp)x while reflect the basic curve in the Y axis.

y=-a(exp)x will reflect the basic curve in the x axis.

y=a(exp)x-h +k will shift the basic curve by reading the h value as opposite, and k values as it is.

remember: increasing function when a > 1.

decresing function when 0 < a < 1.

NOTE: (1/a)(exp)m = 1/a(exp)m = a(neg.exp)m = 1(exp)m/a(exp)m

Example: f(x) = 2(exp)x

Start by making a table of values.

So, while positive x-values give us values like these:

negative x-values give us values like these:

together the reasonable points would be something like this:

And the graph should look something like this:

NOTE: when X is negative, reflect in Y.

when Y is negative, reflect in X.

The homework for today in to finish the assignment Mr.P gave us in class. I wasn't sure how to put the exponents so i put (exp). Thank you for listening to me and i should probably get some rest because basketball tryouts are tomorrow.