2.3 Analyzing Graphs of Functions Here is what you need to do College Algebra N.DeHerrera Look at this power point Do the “Try these” examples, you have the answers at the bottom of the page. Go to class ready to with the “Try these” problems worked out ready to submit. Be prepared to work on some new problems in class before leaving. Sorry, I could not find good videos for this topic.

2.3 Analyzing Graphs of Functions range domain Find the domain and range of the relation. The x-values of the points on the graph include all numbers between  3 and 3, inclusive. The y- values include all numbers between  2 and 2, inclusive. Domain = [  3, 3] Range = [  2, 2] Objective I: The Graph of a Function College Algebra N.DeHerrera

2.3 Analyzing Graphs of Functions Find the domain and range of the relation. Domain: ( ,  ) Range: ( ,  ) College Algebra N.DeHerrera

2.3 Analyzing Graphs of Functions Find the domain and range of the relation. Domain: ( ,  ) Range: [3,  ) College Algebra N.DeHerrera

2.3 Analyzing Graphs of Functions Find the domain and range of the relation. The function has a point of discontinuity at x = 4. Thus it is continuous over the intervals ( , 4) and (4,  ). College Algebra N.DeHerrera

2.3 Analyzing Graphs of Functions a. b. Use the vertical line test to determine whether each relation graphed is a function. Graph (a) fails the vertical line test, it is not the graph of a function. Graph (b) represents a function. College Algebra N.DeHerrera

2.3 Analyzing Graphs of Functions College Algebra N.DeHerrera

2.3 Analyzing Graphs of Functions College Algebra N.DeHerrera

2.3 Analyzing Graphs of Functions College Algebra N.DeHerrera

2.3 Analyzing Graphs of Functions Objective III: Increasing and Decreasing Functions Suppose that a function f is defined over an interval I. If x 1 and x 2 are in I, (a) f increases on I if, whenever x 1 < x 2, f(x 1 ) < f(x 2 ); (b) f decreases on I if, whenever x 1 f(x 2 ); (c) f is constant on I if, for every x 1 and x 2, f(x 1 ) = f(x 2 ). College Algebra N.DeHerrera

2.3 Analyzing Graphs of Functions College Algebra N.DeHerrera

2.3 Analyzing Graphs of Functions Determine the intervals over which the function is increasing, decreasing, or constant. On the interval ( ,  1) the y- values are decreasing. On the interval [0.5, 1], the y- values are increasing. On the interval [1,  ) the y-values are constant. College Algebra N.DeHerrera

2.3 Analyzing Graphs of Functions Determine the intervals over which the function is increasing, decreasing, or constant. Increasing on (0,  ) Decreasing on ( , 0) College Algebra N.DeHerrera

2.3 Analyzing Graphs of Functions Determine the intervals over which the function is increasing, decreasing, or constant. Increasing on (-2,  ) Decreasing on ( , -2) College Algebra N.DeHerrera

2.3 Analyzing Graphs of Functions Determine the intervals over which the function is increasing, decreasing, or constant. f(x)= x 3 -3x Increasing: (-∞,-1) Decreases: (-1,1) Increasing: (1,∞) College Algebra N.DeHerrera 1 -2 (-1,2) (1,-2)

2.3 Analyzing Graphs of Functions Determine the intervals over which the function is increasing, decreasing, or constant. f(x)= x 3 -3x 2 +2 Increasing: (-∞,0) Decreasing: (0,2) Increases: (2,∞) College Algebra N.DeHerrera 2 -2 (0,2) (2,-2)

2.3 Analyzing Graphs of Functions College Algebra N.DeHerrera

2.3 Analyzing Graphs of Functions College Algebra N.DeHerrera

2.3 Analyzing Graphs of Functions Objective IV: Even and Odd functions College Algebra N.DeHerrera

2.3 Analyzing Graphs of Functions Decide whether the function is even, odd, or neither. 1) f(x) = 4x 4  x 2 Replacing x in f(x) = 4x 4  x 2 with  x gives Since f(  x) = f(x) for each x in the domain of the function, f is even. College Algebra N.DeHerrera

2.3 Analyzing Graphs of Functions Try These: Decide whether the function is even, odd, or neither. 1) f(x) = 4x ) f(x) = -4x 5 + 7x 3 3) f(x) = 5x 4 + 5x - 2 4) f(x) = 4x ) f(x) = 3x 3 - 2x Answers: 1) Even2) Odd3) Neither 4) Even 5) Neither College Algebra N.DeHerrera