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Precal Chapter 1 Tes
| Term | Definition |
|---|---|
| function | A function from set D to a ser R is a rule that assigns to every element in D a unique element in r. |
| domain | all the input or x values for a function |
| range | all the output values of a function (y values) |
| function notation | y =f(x) which reads y equals of of x OR the value of a function at x |
| independent variable | x value (x variable) |
| dependent variable | y value (y variable) |
| mapping | a function can be viewed as a ___________ of elements of the domain onto the elements of the range |
| Increasing function (on an interval) | for any 2 points in the interval. a positive change in x results in a positive change in y. (as x increases so does y) |
| Decreasing function (on an interval) | for any two points in the interval, a positive change is x results in a negative change in y (as x gets bigger, y gets smaller) |
| Constant function (on an interval) | if for any two points on the interval a positive change in x results in zero change in f(x). (as x gets bigger, y stays the same) - horizontal line |
| local maximum of a function | a value of a function F9c) that is greater than or equal to the range of values of f on some open interval containing c. It's the top of a peak. |
| Local minimum of a function | a value of a function f(c) that is less than or equal to all range values of f on some open interval containing c. If c is less than or equal to all range values on that interval. |
| absolute maximum | If f(c) is GREATER than or equal to ALL range values in the function. |
| absolute minimum | A value LESS than or equal to ALL values in the range of f. |
| relative extrema | local extrema (this is a relative maximum or relative minimum) |
| even function | a function with symmetry about the y axis. Algebraically f(-x) = f(x) |
| odd function | a function with symmetry with respect to the origin (0,0). Algebraically f(-x) = - f(x). |
| Solve equations algebraically | Find all factors (factor the polynomial). Set each factor equal to zero and solve. This gives you the zeros, roots or solutions (3 words for the same item). |
| What is the shape of a quadratic (highest degree is 2)? | A quadratic is a parabola (shaped like a U opening up or down |
| What shape is a function in this form...y=mx+b or Ax +By=C | Line |
| polynomial | A function with more than one monomial term. A binomial has 2 terms, a trinomial has 3 terms - these are polynomials as well as functions with more than 3 terms. Poly - means many |
| Quadratic Formula | A way of factoring using a formula that will ALWAYS work to find factors (know the actual formula and be able to use it). A way to solve a quadratic formula. |
| Finding the Domain of a function - what to exclude? | 1. exclude any values that cause division by zero 2. exclude any values that result in a negative value under a square root |
| In interval notation what symbol indicates an INCLUDED value | [ or } |
| In interval notation what symbol indicates a value that is NOT included? | ( or ) |
| When graphing a function how do we indicate a value NOT included on a graph? | open circle |
| When graphing a function (or interval on a number line) how do we indicate a VALUE that IS included? | closed circle |
| ordered pair | indicates a point on the rectangular coordinate system (cartesian plane) written as (x, y) |
| solving inequalities - special rule to remember | when multiplying or dividing by a negative number we flip the inequality sign |
| factoring - why is it important? | Remember to practice factoring polynomials, we need this in order to find domain and range (exclude values that made denominators zero) Also important in finding solutions/zeros or roots -- all these mean the same thing--- for polynomials |
| These <,> are called? | inequality symbols |
| Practice Interval notation | This is found in section P.1. Go there and review pages 3,4,5 |
| variable | a letter or symbol that represents a real number (we use x and y alot) |
| constant | a letter or symbol that represents a real number... like this -2, 0, square root of a value, or pi |
| algebraic expression (how is this different from an equation?) | a combination of variables and constants involving addition, subtraction, multiplication, division, powers and roots. |
| real number (sometimes this a solution for domain) | All values between negative infinity and positive infinity (whole numbers, 0 and all decimals) Examples are -8, 1.75, 2.33333 |
| Be able to evaluate a function at any given value | If given a function f(x), evaluate f(3), plug in 3 everywhere there is an x and solve. |
| Be able to compare/match algebraic, numeric and graphical models | This is like problems at the end of section 1.1 |
| Be able to find and explain domain and range | Find this information and examples in section 1.2 in our book. Practice the example problems |
| Practice using Desmos or your TI84 to graph functions | look at questions 9-16 in section 1.2 - remember odd answers are in the back so you can check your work - solve algebraically and graphically |
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