Unformatted text preview: x 1 2 3 4 x −1 f (x) > g (x) The preceding example demonstrates the following, which is a consequence of the Fundamental
Graphing Principle for Functions.
Graphical Interpretation of Equations and Inequalities
Suppose f and g are functions.
• The solutions to f (x) = g (x) are precisely the x values where the graphs of y = f (x) and
y = g (x) intersect.
• The solutions to f (x) < g (x) are precisely the x values where the graph of y = f (x) is
below the graph of y = g (x).
• The solutions to f (x) > g (x) are precisely the x values where the graph of y = f (x) above
the graph of y = g (x).
The next example turns the tables and furnishes the graphs of two functions and asks for solutions
to equations and inequalities. 156 Linear and Quadratic Functions Example 2.4.2. The graphs of f and g are below. The graph of y = f (x) resembles the upside
down ∨ shape of an absolute value function while the graph of y = g (x) resembles a parabola. Use
these graphs to answer the following questions.
y
4
y = g (x) 3
(−1, 2) (1, 2) 2
1 −2 −1 1 2 x −1
y = f (x) 1. Solve f (x) = g (x). 2. Solve f (x) < g (x). 3. Solve f (x) ≥ g (x). Solut...
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 Fall '13
 Wong
 Algebra, Trigonometry, Cartesian Coordinate System, The Land, The Waves, René Descartes, Euclidean geometry

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