Functions 10.1 Describing Functions

Chapter 10 Functions 10.1 Describing Functions A function is like a machine that converts numbers into other numbers. Functions are often named with the letters f, g, and h. If function f converts the number 2 into the number 7, we write f(2) = 7. Functions can be described with an equation, a graph, or a list of ordered pairs. 10.1 Describing Functions If the function g is defined as g={(1,7), (2,9), (3,11), (4,13), (5,15), (6,17), (7,19)}, what is the value of g(7)? Since the ordered pair that has a 7 as the first coordinate is (7,19), this means that g(7)=19. 10.1 Describing Functions Domaines are x coordinates. Ranges are y coordinates. When asked to find the domains or ranges, you will look at the x or y values. What is the domain of function h = {(2,5),(4,17),(7,50)}? Answer: {2,4,7} What is the range of function h = {(2,5),(4,17),(7,50)}? Answer: {5,17,50} If the range is repeating like this: h = {(2,5),(4,17),(7,5)}? Then you will write skip repeating the range: {5,17} It’s okay to have repeating y-values, it will still be a function. It’s NOT okay to have repeating x-values, then it will NOT be a function. Do question 8 on page 303 10.2 Function Graphs A list of ordered pairs is not always the most efficient way to describe the input and output values of a function. A graph of these values is especially useful when there are an infinite amount of numbers in the domain of the function. The function graph can be used to evaluate the function at different values and can also be used to determine the domain and range of the function. 10.2 Function Graphs When questions ask you to find the value of f(2) on a graph, that means they are looking for a point on the graph that crosses x-value of 2. It will be f(2)= 1 Your x value is 2 and y value is 1, which makes its (2,1) or f(2)=1 10.2 Function Graphs Let’s understand example 4 on page 308. “Which of the following can be the graph of a function?” There are 4 different graphs here. We have to find a graph that is a function. Remember, if the y-values are repeating, then the graph can still be considered a function, however, if the x-values are repeating then your graph is NOT a function. So here we can see only number 3 is a function because x-value repeats ONCE. There’s one test you can do to value your graph is a function. Draw a vertical line through your graph, you can draw multiple vertical lines. If the vertical line crosses or touches your x-value more then once, the it’s not a function. 10.2 Function Graphs Read page 310. The first graph shows how to find your domains and ranges, remember, domains are x-values, ranges are y-values. Here your domains are 1, 7, and every number between 1 and 7. Why? Because you have a graph line that has limit, it’s not ongoing. You can write your domains as 1 less than or equal to x less than or equal to 7. Same strategy applies for defining your ranges. Now, the second graph shows a line with one dot and two ongoing arrows. That mean it’s an infinite number graph, where you have all real numbers. {-♾,♾} 10.2 Function Graphs Go to page 312, and let’s do questions 2, 3, 4, and 6. HOMEWORK :( Page 314 Q. A9 Page 315 Q. A10 Page 316 Q. B3