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Functions and mappings

5.2 Notes

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5.2 ? Functions and Function Notation Consider the following set: Domain: Range: A function is like a machine, you put a number in (input or _________), the machine mashes it, stretches it, etc. and the machine spits out a new number (output or __________). This is a special type of relation because for every input there is only one output. (eg. If you put 3 into the machine, it will always output 6) ?Every function is a relation but not every relation is a function.? Example 1 then output first Multiply by 3 Add 2 input Equation Graph Ordered Pairs Table of Values Input Output -3 -1 0 1 3 Determining whether a relation is a function: {(1, 2), (0, 5), (3, 8), (-3, 2), (5, 9)}Example 2 b) -2 3 6c)

Relations and Functions Final Review

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3 6 9 12 15 18 21 24 27 30 33 36 39 42 45 48 t (Min) 1 2 3 4 5 6 d (km) 1 2 3 4 5?1?2?3?4?5 x 1 2 3 4 5 ?1 ?2 ?3 ?4 ?5 y Relations and Functions Practice Questions 1. The following distance-time graph represents the distance (in kilometres) a person bicycled during a 50-min period. Describe a possible scenario. 2. The table of values shows the cost of movie tickets at a local theatre. Number of Tickets Cost ($) 1 12 2 24 3 36 4 48 (a) Is this a linear or non-linear relationship? Explain how you know. (b) Assign a variable to represent each quantity in the relation. Which variable is the dependent variable and which is the independent variable?

Chapter 11: Relations and Functions Test

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Name: _______________ Date: _______________Relations and Functions Practice Test Multiple Choice (1 mark each) Use the following information to answer the next question. A farmer read a study of soil fertility and mineral absorption. It contained the graph below. The graph illustrates the relative absorption of copper by the top and bottom of a wheat plant when the plant was subjected to various solutions containing a fixed amount of copper but having different concentrations of aluminum. From this graph, the farmer concluded that the relative absorption of copper consistently decreased at the A top of a wheat as the aluminum concentration increased B top of a wheat as the aluminum concentration decreased C bottom of a wheat as the aluminum concentration increased

Precalculus Functions Anecdotes

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1. Identity Function-This is the only function thats acts on every real number by leaving it alone 2. Square Root Function-Put any positive number into your calculator. Take the square root. Then take the square root again, and so on. Eventually you will always get 1. 3. Squaring Function-The graph of this function, called a parabola, had a reflection property that is useful in making flashlights and satellite dishes. 4. Cubing Function-The origin is called a ?point of inflection? for this curve because the graph changes the curvature at the point. 5. Reciprocal Function-This curve, called a hyperbola, also has a reflection property that is useful in satellite dishes. 6. Natural Log Function-This function increases very slowly. If the x-axis and y-axis

Inverse Functions

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Inverse Functions Given a function , if there is a function such that which equals the identity function The function is said to be "invertible" "undoes" what "does", and vice versa Such a function is called the inverse, denoted as (the inverse of ) The notation is not to be confused with an exponent In some cases the inverse of a function can be found through algebraic methods CONSIDER: Given to determine we must find a functions that must undo But, recall the set of outputs from , to undo we take Thus Observe that: Not every function has an inverse CONSIDER: But is not a function. An inverse only exists when different inputs in the domain always yield different outputs in the range Such functions are called one-to-one

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