Lesson 3.1 Read: Pages 196-202 3.1 Handout #1-11 (ODD), 15-19 (ODD), 23-43 (EOO), 45-57 (ODD), 63-71 (EOO)

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Presentation transcript:

Lesson 3.1 Read: Pages Handout #1-11 (ODD), (ODD), (EOO), (ODD), (EOO)

Exponential Equations and Functions Objective Students will know how to recognize, graph, and evaluate exponential functions.

Solve for x.

Graph the following functions on the same graph. What is the relationship between the two graphs? Explain algebraically.

Sketch a graph. Be sure to label at least one key point and show any asymptotes.

f(x) = ab x-h + k What will the values of h and k do the graph of f(x) = ab x ? h will shift the graph h units horizontally and k units vertically.

Graphs of Exponential Functions Step 1: Step 2: Use your value of k (vertical shift) to relocate your horizontal asymptote. Use your transformations to relocate the point (0,1). (in the form f(x) = ab x-h + k) Step 3: Plot a point to the right and left of the relocated point (0,1). Step 4: Sketch your graph.

Sketch the graph of the function. (a) Clearly label any intercept(s) and/or asymptotes (b) Label the transformation of the point (0,1) (c) State the domain and range of the function (d) State whether the graph is increasing or decreasing

Sketch the graph of the function. (a) Clearly label any intercept(s) and/or asymptotes (b) Label the transformation of the point (0,1) (c) State the domain and range of the function (d) State whether the graph is increasing or decreasing

Find the exponential function of the form that passes through the points (0,3) and (2,108).

What is e ? Natural base e (Euler Number)

As n gets larger, gets closer to … What type of number is e ?

As n approaches +∞, approaches e. The Natural Base e

True or False?

Sketch the graph of the function. (a) Clearly label any asymptotes (b) Label the transformation of the point (0,1) (c) State the domain and range of the function