Lesson 1: 6-1 Graphing Exponential Functions

How do you determine whether the function y=b^x is increasing or decreasing?
What is the y-intercept?
How do you determine the equation for the horizontal asymptote?

exponential function
exponential growth
asymptote
growth factor
exponential decay
decay factor

A.CED.2 Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales
F.IF.4 For a function that models a relationship between two quantities, interpret dey features of graphs and tables in terms of the quantities, and sketch graphs showing key features given a verbal description of the relationship.
F.IF.7e Graph exponential and logarithmic functions, showing intercepts and end behavior, and trigonometric functions, showing period, midline, and amplitude.
F.IF.8.b Use the properties of exponents to interpret expressions for exponential functions
F.BF.3 Identify the effect on the graph of replacing f(x) by f(x)+k, kf(x), f(kx) and f(x+k) for specific values of k; find the value of k given the graphs. Experiment with cases and illustrate an explanation of the effects on the graph using technology.

see below

The function f(x)=b^x, where b is a positive real number and b does not equal 1, is an exponential function. When b>1, the function has no x intercepts and on y intercept. It is an increasing function with a horizontal asymptote. When 0<b<1, the function has no x intercepts and one y intercept. It is a decreasing function with a horizontal asymptote.

If you see a funny video online and share it with 100 of your friends, and each of your friends shares the video with 100 of their friends, the number of people who see the video increases exponentially until you can say that the video has gone viral. The equation y=100^x can be used to represent this situation where x is the number of rounds that the video has been shared.

Be sure to not confuse y=x^2 with y=2^x. One is a polynomial, while the other is exponential

Ask students where they have heard the term exponential before and what they think it might mean. Students may have heard terms like exponential growth on a television news program and they might think that exponential means enormous. Use students' answers to introduce the concept of exponential functions.

Use McGraw Hill resources

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