1. Section 2.1
Functions

2. Evaluating functions f(x) = F(0) = (02 – 1) / (0 + 4) = -1/4
F(-x) = (-x2 – 1) / (-x + 4) = (x2 -1)/(-x + 4)
-F(x) = (x2 – 1) / (x + 4) = (-x2 + 1)/(x +4)
F(x + 1) = ((x + 1)2 – 1) / (x ) = (x2 + 2x)/(x + 5)
F(2x) = ((2x)2 – 1) / (2x + 4) = (4x2 – 1)/(2x + 4)
F(x + h) = ((x + h)2 – 1) / (x + h + 4) = (x2 + 2xh + h2 – 1)/(x + h + 4)

3. Evaluating functions Practice: f(x) = |x| + 4 F(0) = |0| + 4 = 4
F(-x) = |-x| + 4 =|x| + 4
-F(x) = -(|x| + 4) = -|x| - 4
F(x + 1) = |x + 1| + 4
F(2x) = |2x| + 4 = 2|x| + 4
F(x + h) = |x + h| + 4

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6. Summary Important Facts About Functions
For each x in the domain of f, there is exactly one image f(x) in the range; however, an element in the range can result from more than one x in the domain.
f is the symbol that we use to denote the function. It is symbolic of the equation that we use to get from an x in the domain to f(x) in the range.
If y = f(x), then x is called the independent variable or argument of f, and y is called the dependent variable or the value of f at x.
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7. f(x) + g(x) or (f + g)(x) means to add the two expressions of f and g together and simplify.
f(x) – g(x) or (f – g)(x) means to subtract the two expression of f and g together and simplify
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8. f(x) ● g(x) or (f ● g)(x) means to multiply the two expressions of f and g together and simplify
f(x)/g(x) or (f ÷ g)(x) means to divide the two expressions of f and g together and simplify

9. Examples
Use the functions to find the following f(x) = x - 1 and g(x) = 2x2 , and find the domain
a) (f + g)(x) b) (f – g)(x) c) (f • g)(x) d) (f/g)(x)
Use the same functions to find the following.
a) (f + g)(3) b) (f – g)(4) c) (f • g)(2) d) (f/g)(1)

10. Practice
Use the functions to find the following and find the domain f(x) = √x and g(x) = 3x – 5
a) (f + g)(x) b) (f – g)(x) c) (f • g)(x) d) (f/g)(x)
Use the same functions to find the following.
a) (f + g)(3) b) (f – g)(4) c) (f • g)(2) d) (f/g)(1)

11. Copyright © 2013 Pearson Education, Inc. All rights reserved