Chapter 1 Notes

1. Chapter 1 Notes Graphs of functions are the collections of ___________________ Where x is the ___________of the function, also called the __________ of the function f And f(x) is the ____________of the function (y-value) Section 1.3 Graphs of Functions

2. 1.3 Notes (continued) • A graph of function f is shown • Use the picture of f to determine the domain ______ • Use the picture to determine the range ______ • Use the picture to find f(2) _____ f(0) _____ f(-1) _____ f(4) _____

3. 1.3 Notes (continued) • Finding Domain and range of a function • If • What is the domain? • What is the range? • Check your result graphically

4. 1.3 Notes (continued) • Testing of Graphs for Functions • Use the Vertical Line Test VLT – Which of the following graphs are functions?

5. 1.3 Notes (continued) • Increasing, Decreasing, or Constant • A function is __________on an interval if, for any x1 and x2, in the interval, ________________________ • A function is __________on an interval if, for any x1 and x2, in the interval, ________________________ • A function is ________on an interval if, for any x1 and x2, in the interval, __________________ • In other words • Increasing – ____________________ • Decreasing – ___________________ • Constant – __________________

6. 1.3 Notes (continued) • Shown to the right is a graph of a function f. • On what interval(s) is f increasing, decreasing, and/or constant? • Increasing • Decreasing • Constant

7. 1.3 Notes (continued) • Shown to the right is a graph of a function f(x) = x3-3x • On what interval(s) is f increasing, decreasing, and/or constant? • Increasing ______ • Decreasing ______ • Constant ______

8. 1.3 Notes (continued) Minimums and Maximums A function’s value f(a) is a called a _________________of f if there exists an interval (x1,x2) that contains a such that ____________________ A function’s value f(a) is called a ________________of f if there exists an interval (x1,x2) that contains a such that ____________________

9. 1.3 Notes (continued) • In General, a function can have any number of relative mins/maxs • Some functions may have what is called an ABSOLUTE maximum or minimum • Where that particular value of the function is the maximum or minimum over the entire domain of the function.

10. 1.3 notes (continued) • Finding relative mins/maxs using calculator. • Approximate any relative minimums or maximums of

11. 1.3 Notes (continued) • Sketching a Piecewise graph by hand.

12. 1.3 Notes (continued) • Even, Odd, or Neither. • A function is said to be an ________Function if • Even functions are symmetric about the y-axis • Or, each value of x and it’s opposite (-x) give the same value of the function. • A function is said to be an ________Function if • Odd functions are symmetric about the origin • Or, each value of x and it’s opposite (-x) give the opposite value of the function.

13. 1.3 Notes (continued) • Is f(x) even, odd or neither? • So, • Graphically -

14. 1.3 Notes (continued) • Is g(x) even, odd or neither? • So, • Graphically -