Flashcards: Graphing Exponential Functions — 11 cards

What is the form of an exponential function?

An exponential function has the form $f(x)=b^x$ with positive base $b$.

Exponential function symbol

f(x)=b^x, with b > 0

When does $y=ab^x$ represent exponential growth?

It represents exponential growth when $b>1$ and $a>0$.

Growth condition on b

b > 1 for growth, 0<b<1 for decay

What is the domain of the graph of $f(x)=2^x$?

All real numbers.

Graph of f(x)=2^x

Domain all reals; y-intercept (0,1); asymptote y=0

How does $f(x)=2^x$ behave as x approaches negative infinity?

It approaches 0.

Asymptote of exponential graphs

Horizontal line y=0

Transform formula

$f(x)=ab^{x-h}+k$

Order of transformations

Reflect/scale, shift h, then shift k

Exponential growth model formula

A(t)=a(1+r)^t