THE DOMAIN AND RANGE OF A FUNCTION Basically, all functions do is convert inputs into outputs.

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1 THE DOMAIN AND RANGE OF A FUNCTION Basically, all functions do is convert inputs into outputs. Exercise #1: Consider the function y = f (x) shown on the graph below. (a) Evaluate each of the following: (b) Can the function rule, given by the graph, give you a value when x = 5? If so, what is it? If not, why not? (c) Is x = 5 in the domain of the function? (d) Give two other values of x that are not in the domain of the function. (e) Circle the following y values that are in the range of the function? Show evidence on your graph. (f) Write the domain and range of this function using a single inequality. DOMAIN RANGE 1

2 Exercise #2: Given the function Write the set in roster notation. and the domain shown below, fill in the range. Range: 2

3 Exercise #3: Which of the following values is not in the domain of the function f ( x) shown below? Illustrate your thinking by marking points on the graph. 3

4 Exercise #4: Consider the piecewise linear function given by the formula (a) Graph the function. State the domain. (b) Determine the function s range. 4

5 Exercise #5: The following graph represents the height above the ground versus time at a resort as Thomas rides his favorite ski slope. (a) State the domain and, in your own words, what the domain represents. (b) State the range and, in your own words, what the range represents. (c) What might Thomas have been doing for the interval 0 t 2? What was his average rate of change? Use proper units in your answer. (d) What might Thomas have been doing for the interval 2 t 6? What was his average rate of change? Use proper units in your answer and compare to what you found in (c). 5

6 Exercise #6: The graph below represents the height of a ball over the interval 0 t 8. (a) After how many seconds was the ball 12 feet off of the ground? Explain your answer. (a) What does your answer indicate about the range of this function? 6

7 Exercise #7: State the range of the function Show the domain and range in the mapping diagram below. if its domain is the set 7

8 Exercise #8: The function is completely defined by the graph shown below. Answer the following questions based on this graph. (a) Determine the minimum and maximum x values represented on this graph. (b) Determine the minimum and maximum y values represented on this graph. (c) State the domain and range of this function using interval notation. 8

9 Some functions, defined with graphs or equations, have domains and ranges that stretch out to infinity. Exercise #9: The function is graphed on the grid below. Which of the following represent its domain and range written in interval notation? 9

10 For most functions defined by an algebraic formula, the domain consists of the set of all real numbers. Sometimes, though, there are restrictions placed on the domain of a function by the structure of its formula. Exercise #10: The function table. has outputs given by the following calculator (a) Evaluate from the table. f (1) and f (6) (b) Why does the calculator give an ERROR at x = 4? (c) Are there any values except x = 4 that are not in the domain of f? Explain. 10

11 Exercise #11: Which of the following values of x would not be in the domain of the function Explain your answer. 11

12 Exercise #12: Which of the following represents the range of the quadratic function shown in the graph below? 12

13 Daily Learning Outcome: I know how to graph a function using the graphing calculator and how to identify graphical features of functions. THE DOMAIN AND RANGE OF A FUNCTION Graphs are one of the most powerful ways of visualizing a function s rule because you can quickly read outputs given inputs. You can also easily see features such as x intercepts, y intercepts, turning points, increase or decrease for a given domain. 13

14 THE DEFINITION OF A FUNCTION A function is a clearly defined rule that converts an input into at most (no more than) one output. These rules often come in the form of: (1) equations, (2) graphs, (3) tables, and (4) verbal descriptions. 14

Sect 4.5 Inequalities Involving Quadratic Function

Sect 4.5 Inequalities Involving Quadratic Function 71 Sect 4. Inequalities Involving Quadratic Function Objective #0: Solving Inequalities using a graph Use the graph to the right to find the following: Ex. 1 a) Find the intervals where f(x) > 0. b) Find