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Introduction to Parent Functions - Algebra II

Learn about different types of parent functions such as constant, linear, quadratic, cubic, and square root functions. Understand domains, ranges, plotting points, and transformations. Practice evaluating functions and graphing on a calculator.

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Introduction to Parent Functions - Algebra II

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  1. Algebra II Section 1.2 Introduction to Parent Functions

  2. Warm-up #1 For the power , identify the exponent and the base #2 Evaluate #3 Evaluate f(9) when

  3. Function-a relation in which every input (x) is paired with exactly one output (y or f(x)) each x has a unique y y may be paired with more than one x

  4. http://www.youtube.com/watch?v=sE4eq0cjLFk

  5. Relation- set of ordered pairs each x does not necessarily have a unique y

  6. Domain- set of all possible input values in a relation or function (independent variable) • Range- set of all possible output values in a relation or function (dependent variable)

  7. https://www.youtube.com/watch?v=VUTXsPFx-qQ

  8. Parent Functions #1 Constant Function y= constant f(x) = constant Graph is a horizontal line Domain- all real numbers Range- the constant in the equation

  9. #2 Linear Function y=x f(x) = x Graph is a straight line. Domain- all real numbers Range- all real numbers

  10. #3 Quadratic function y= f(x) = Graph is a parabola. Domain- all real numbers Range- {yy 0}

  11. #4 Cubic function y= f(x) = Graph looks like the union of the right side of an up parabola and the left side of a down parabola Domain- all real numbers Range-all real numbers

  12. #5 Square root function y = f(x) = Graph looks like the top half of a parabola turned to the right. Domain= {x|x 0} Range= {y|y 0}

  13. Minimum number of points to make a good graph

  14. You can make a table to graph a function. • It is helpful to remember the shape of the parent function. • Remember the number of points needed for each type of function.

  15. You need to build a table. Make sure you have all the necessary columns! bad good

  16. Table

  17. Plot the points from your table and you have one of the parent graphs

  18. Graph • What parent function will this belong to? • What needs to be in the table? • How many points do we need? • Plot the points. • Connect the dots! • Do the graph look like the parent function? • What is the transformation?

  19. Try these Pg. 18 #1-7 After discussion Pg. 18 #8,9,10

  20. When a graph is a transformed, the domain and range may change.

  21. Classwork/homework #2 Pg. 19 #11-15,24-27, 42-46

  22. You can use the graphing calculator to make a graph. • All graphing keys are on the top row on the calculator.

  23. Graphing parent functions and transformations Step 1 Set up graph paper on the calculator The most common window is shown below.

  24. Graphing calculator Setting up a window is like drawing a grid on graph paper.

  25. Step 2 Type the equation into y= Press graph

  26. Typing in the equation • There is an x key (next to the alpha key) • If you need a negative sign (it is on the bottom row). Do not use the subtraction sign! • There is a squared key. For any exponent bigger than two use the carrot key (below clear)

  27. Finding some points on the graph • Press table set • You can pick a start number for x • You can decide ∆table • What does the symbol ∆ mean here? • Using the arrow keys will give you an infinite number of points.

  28. Try these! • Pg. 19 #17-22 • Graph the equation on the calculator. • Find five points on the graph using the table. • Duplicate the graphs on graph paper.

  29. You can graph more than one equation on the calculator • Type 1st equation into • Type 2nd equation into

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