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: Chapter 5, Lesson 2, page 209.
Exponents and More!
Exponents and More with Exponents
Remember, an exponent tells how many times we use a base as a factor. For example, `a^3=a⋅a⋅a`. An expression written with exponents is written using exponential notation.
For like bases, we have:
- Rule: `a^0=1`
- Rule: to multiply we do `a^m⋅a^n=a^(m+n)
- Rule: to divide, we do `a^m/a^n=a^(m-n)`
- Rule: for negative exponent, we can express them as positive by, `a^(-m)=1/a^m
- Rule: for raising a power to another power, `(a^m)^n=a^(mn)`
- Rule: for raising a product to a power, `(ab)^n=a^n⋅b^n`
- Rule: for raising a quotient to a power, `(a/b)^n=a^n/b^n`
Remember and MEMORIZE THESE RULES for Lessons 1 and 2. Practice here!
They are also included in the Algebra Cheat Sheet that was passed today. As long as you remember these 7 formulae, you’ll be OK. Remember, if you forget the rules, just write out the problem and see what can be simplified!
PurpleMath has an EXCELLENT 2 page tutorial, click here!
Two of tonight’s homework problems solved by MrE are here! Just click it.
Two of tonight’s homework problems solved by MrE are here! Just click it.