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**Unformatted text preview: **The next example motivates the core ideas.
Example 2.4.1. Let f (x) = 2x − 1 and g (x) = 5.
1. Solve f (x) = g (x).
2. Solve f (x) < g (x).
3. Solve f (x) > g (x).
4. Graph y = f (x) and y = g (x) on the same set of axes and interpret your solutions to parts 1
through 3 above.
Solution.
1. To solve f (x) = g (x), we replace f (x) with 2x − 1 and g (x) with 5 to get 2x − 1 = 5. Solving
for x, we get x = 3.
2. The inequality f (x) < g (x) is equivalent to 2x − 1 < 5. Solving gives x < 3 or (−∞, 3).
3. To ﬁnd where f (x) > g (x), we solve 2x − 1 > 5. We get x > 3, or (3, ∞).
4. To graph y = f (x), we graph y = 2x − 1, which is a line with a y -intercept of (0, −1) and a
slope of 2. The graph of y = g (x) is y = 5 which is a horizontal line through (0, 5).
y
8
7
6 y = g ( x) 5
4
3
2 y = f (x) 1 1 2 3 4 x −1 To see the connection between the graph and the algebra, we recall the Fundamental Graphing
Principle for Functions in Section 1.7: the point (a, b) is on the...

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