Solving Equations and Inequalities by Graphing

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Chapter 2

• Section 4
• Solving Equations and Inequalities by Graphing

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Homework

• Assignment 6 due September 12
• Read Section 2.4
• In Section 2.4 do 1,4,7,10,16,17,22,28,33 and 37.
  On 37 use the ZERO in the CALC menu.

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Comparing Functions

• Our primary goal in this section is to compare
  two functions at interesting values

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Example

• Compare these functions at x -2, 0 , and 3.
  Graph both f and g on your calculator and use the
  graphs to verify your results.

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Comparing Functions Using Their Graphs
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Summary
The solution of the equation f(x) g(x) is the
set of all x for which the graphs of f and g
intersect. The solution of the inequality f(x) lt
g(x) is the set of all x for which the graph of
f lies below the graph of g. The solution of the
inequality f(x) gt g(x) is the set of all x for
which the graph of f lies above the graph of g.
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Example
Find all x such that
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Your Turn Use the Supplied Graph Paper
Find all x such that
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Using the Calculator (page140)

• Use the graphing calculator to solve
• Note that what we want to do is solve

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Another Example
i. Load each side of the inequality into the Y
menu of your calculator. Adjust the WINDOW
parameters so that the point(s) of intersection
of the graphs is visible in the viewing window.
Use the intersect utility in the CALC menu of
your calculator to determine the coordinates of
the point(s) of intersection. ii. Make an
accurate copy of the image in your viewing window
on your homework paper. Label and scale each axis
with xmin, xmax, ymin, and ymax, and label each
graph with its equation. iii. Draw a dashed,
vertical line through the point(s) of
intersection. Shade and label the solution of the
inequality on the x-axis. Use both set-builder
and interval notation to describe the solution
set.
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Comparing Functions with Zero

• When we evaluate a function at a value of x, only
  three outcomes are possible

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i. Make an accurate copy of the image on graph
paper, drop dashed, vertical lines through the
x-intercepts, then label and shade the solution
of f(x) gt 0 on the x-axis. Use set-builder and
interval notation to describe your solution
set. ii. Make a second copy of the image on graph
paper, drop dashed, vertical lines through the
x-intercepts, then label and shade the solution
of f(x) lt 0 on the x-axis. Use set-builder and
interval notation to describe your solution set.
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Chapter 2

• Section 5
• Geometric Transformations

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Lets Play

• Load the following function into your calculator.
  Graph by generating atable of points.

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• If y f(x) is the graph we just plotted, then
  graph y 2f(x) by using the table of points we
  already generated.

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• If y f(x) is the graph we just plotted, then
  graph y 1/2f(x) by using the table of points we
  already generated.

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Scaling
If a gt 1, then the graph of y af(x) is
stretched vertically, both positively and
negatively, by a factor of a. If 0 lt a lt 1,
then the graph of y af(x) is compressed
vertically, both positively and negatively, by a
factor of 1/a.