Properties of Elementary Functions

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Presentation transcript:

Properties of Elementary Functions Power Functions

Power Functions - Algebraically Parent Function General Equation: Translated Function:

Power Functions - Graphically There are two things we talk about with each power graph: Concavity (Concave Up or Concave Down) and Direction (Increasing or Decreasing) Concave Down and Increasing Exponent between 0 and 1 Concave Up and Increasing Exponent greater than 1 Concave Up and Decreasing Negative Exponent

Power Function – Domain Restrictions If b>0 then domain is all real numbers If b<0 then the domain excludes x=0 This is because negative exponents make fractions, and we can’t divide by 0 If b is NOT an integer, the domain excludes negative numbers For most real world applications of power functions, we restrict the domain to all positive numbers

Power Functions – Other Graph Information If b>0 our graph contains the point (0, 0) (the origin) If b<0 there are two asymptotes, along the x-axis and y-axis If b>0 the graph is increasing If b<0 the graph is decreasing The graph is concave up if b>1 The graph is concave down if 0<b<1

Power Functions - Numerically Power functions follow a multiplication pattern for both x and y. To check what type of function a table represents you would usually first check linear and quadratic. If it isn’t either of those, you would then check power. Use the y-values that can be multiplied by a constant number to get the next. Exclude any points that don’t follow this pattern for x Check the y-values of these points, they should also multiply by a constant.

Assignment From Yesterday: From Today: Pages 74-75 Problems Q1-Q10 (review of function notation), 11 (parts a&c only), and 13 (parts a&c only) Pages 84-85 Problems Q1, Q4, Q9, 5, 8, 11 and 12 For problems 5-8 determine whether each table is linear or quadratic From Today: Page 76 Problems 17 (parts a-c) and 18 (parts a-c) Pages 84-85 Problems 5, 7 and 10 State whether these three tables represent power functions or not