Algebra: Chapter 12, Lesson 1 and Lesson 2, page 536 and 542.
Relations and Functions and Graphs
A relation is a set or ordered pairs. The domain of a relation is the set of first coordinates (the x’s). The range is the set of second (or y) coordinates.
A function is a relation that assigns one member of the domain EXACTLY one member of the range. In other words, one x can have ONLY one y value.
You can evaluate a function `f(x)=2x^2 + 5` for `f(2)` by substituting 2 for every x that you see. In our example then, `f(2)=2⋅4 + 5 = 13`
You can recognize a function with the vertical line test. You can find the domain and range of a function by seeing where the function is not defined. Good examples are `−`, we can’t take square roots of negative numbers and we cannot have `1/0` because that results in infinity or an undefined solution.
Here again, is a great link for Purplemath.
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Algebra 1a: CST Review
Square Roots: The `sqrt(25) = 5`.
The `sqrt(5)` can be approximated as somewhere between the `sqrt(4)` and the `sqrt(9)`.
`sqrt(9)=3`
`sqrt(5) = ?`
`sqrt(4)=2`, so `sqrt(5)` is closer to `sqrt(4)` than `sqrt(9)`. A good guess could be 2.2?
Pythagorean Theorem: Only works for right – triangles. The 3 sides of the triangle are `a`, `b`, and `c`. `a` and `b` are the short sides and `c`, the side OPPOSITE the right angle is called the hypotenuse.
The theorem states:
`c^2= a^2 + b^2` (if you know the 2 smaller sides, `a` and `b`)
or
`a^2 = c^2 – b^2` (if you know the hypotenuse, `c` and side `b`)
or
`b^2 = c^2 – a^2` (if you know the hypotenuse, `c` and side `a`)