Math 131 Algebra Review, Lecture notes of Algebra

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Review of Algebraic, Exponential,

and Logarithmic Functions

What is a function?

Four representations of a function

1. Verbally
2. Numerically (Table)
3. Visually (Graph)
4. Algebraically (Formula)

Linear Functions and Models 𝑦 = 𝑓 𝑥 = 𝑚𝑥 + 𝑏

Power Functions 𝑓 𝑥 = 𝑥 𝑎 , where 𝑎 is a constant.

Quadratic and Power Functions 𝑓 𝑥 = 𝑎𝑥 2

• 𝑏𝑥 + 𝑐, 𝑎 ≠ 0 𝑓 𝑥 = 𝑥 𝑎 , where 𝑎 is a constant.

Rational Functions 𝑓 𝑥 =

Example: 𝑓 𝑥 = 2 𝑥 4 −𝑥 2

• 1 𝑥 2 − 4

Radical Functions 𝑓 𝑥 = 𝑥 𝑎 , where 𝑎 is a constant.

1 𝑛

Exponent Laws

Special exponential functions

Logarithm Properties

Special Logarithmic Functions

Transformations

2. Stretch, Compress, Reflect

Other algebraic functions:

• Absolute Value Functions