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Algebra II

Algebra II. Section 1.2 Introduction to Parent Functions. Warm-up. #1 For the power , identify the exponent and the base #2 Evaluate #3 Evaluate f(9) when. Function -a relation in which every input (x) is paired with exactly one output (y or f(x)) each x has a unique y

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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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