Chapter 11 Section 2

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Chapter 11 Section 2

• Exponential Functions

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• Homework 14
• 11.1 55, 57 Consult the graph of the given
  function on your calculator. Check to insure that
  the function is one-to-one before continuing. Use
  the procedure outlined at the top of page 714 to
  find the inverse.
• 11.1 65, 67 Set up a table of points satisfying
  each equation. On a sheet of graph paper, plot
  the points from your table, then use them as a
  guide to complete the graph of the given
  equation. Label this graph with its equation.
  Draw the line yx on your graph paper. Reflect
  each of the plotted points across the line yx
  and use them as a guide to complete the graph of
  the inverse equation. Label the graph of the
  inverse with its equation.
• 11.1 71, 77
• Read section 11.2
• 11.2 5, 7, 17, 19 First try to sketch the graph
  of the given exponential function without the aid
  of a calculator. A rough graph is all that is
  expected. Plot the y-intercept and label it, and
  then plot two more points on each side of the
  y-axis. Using the points you've plotted, sketch
  the graph and indicate whether the function
  experiences exponential growth or decay. Also,
  draw the horizontal asymptote as a dashed line
  and label it with its equation. Next graph the
  function on your calculator and check your paper
  sketch. If you made any errors, correct the graph
  on your paper. Use interval notation to describe
  the domain and range of the given exponential
  function.
• 11.2 45 For your graph, be sure to use a window
  which includes all of the data points used in
  parts (a) and (b), and mark those points on your
  graph. Label each axis with xmin, xmax, ymin, and
  ymax.

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Horizontal Line Test for One-to-One Functions

• If a horizontal line intersects a graph once and
  only once for each element of the range, then the
  graph is a one-to-one function.

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• Recall the Laws of Exponents

Page 303
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Exponential Functions

• The function f(x) ax,where a is a positive
  constant and a is not equal to 1, is called the
  exponential function with base a.

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The Rabbit Function
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The Rabbit Function
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The Rabbit Function
Where x is the time unit and f(x) is the number
of Rabbits running around. Load this function
into Y1and look at the graph.
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Decaying Sixs

• Working in as a group well come up and roll all
  of the dice on the floor and remove any 6s.
  After we count how many we removed, well then
  roll the remaining dice and remove any 6s. Well
  repeat this until all the dice are removed. Your
  job is to keep track of the data at each roll.

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Plot Our Data

• Load the data into L1 and L2 and lets look at it

Where x is the number of rolls that have
occurredand n0 is the initial number of dice.
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The Graph of an Exponential Function
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Examples

• Page 857 1 through 4 and39 through 44

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Graph the Following by Hand