Interpreting Graphs and Functions of the

graphs and functions

1. Interpreting Graphs of Functions

2. 4 3 2 1 In addition to level 3.0 and above and beyond what was taught in class,  the student may: · Make connection with other concepts in math · Make connection with other content areas. The student will understand the concept of a function and use of function notation. - Evaluate functions for given inputs. - Interpret key features of graphs and tables of a function. - Sketch graphs of functions. - Determine the domain of the equation or graph of a function and what it may represent in context. - Convert a table, graph, set of ordered pairs, or description into function notation by identifying a rule. - Identify numbers that are not in the domain of a function. [f(x) = 1 / x x ≠ 0 or f(x) = x ≠ a negative] The student will be able to understand the concept of a function. - Correctly use function terminology (domain, range, f(x)). - Determine if a relationship given in a table, graph, or words depicts a function. With help from the teacher, the student has partial success with function terminology, function notation and determining if a relation table or graph depict a function. Even with help, the student has no success understanding the concept of a function. 4 3 2 1 In addition to level 3.0 and above and beyond what was taught in class,  the student may: · Make connection with other concepts in math · Make connection with other content areas. The student will be able to understand the concept of a function. - Correctly use function terminology (domain, range, f(x)). - Determine if a relationship given in a table, graph, or words depicts a function. With help from the teacher, the student has partial success with function terminology, function notation and determining if a relation table or graph depict a function. Even with help, the student has no success understanding the concept of a function. Learning Goal for Focus 3 (HS.A-CED.A.1, HS.F-IF.A.1 & 2, HS.F-IF.B.4 & 5): The student will understand the concept of a function and use of function notation.

3. Parts of a graph… X-intercept – where the graph crosses the x-axis. (x, 0) Y-intercept – where the graph crosses the y-axis. (0, y)

4. Find the x- and y- intercepts of the graph. X-intercepts (-2, 0) and (2, 0) Y-intercept (0, -4)

5. Parts of a graph… Increase – A function is “increasing” when the y-value increases as the x-value increases. Interval – A section of the graph. This function is increasing for the interval shown. It may be increasing or decreasing elsewhere. Decrease – A function is “decreasing” when the y-value decreases as the x-value increases.

6. Find where the function is increasing or decreasing. The graph is increasing in the following intervals: [-2.2, -1.2] [1.2, 2.2] The graph is decreasing in the following interval: [-1.2, 1.2]

7. Parts of a graph… Maximum – the largest value of the function within the interval . What is the maximum value in the interval [1, 5]? The maximum value is 4. Minimum – the smallest value of the function with an interval . What is the minimum value in the interval [1, 5]? The minimum value is 1.

8. Identify the features of the function. Find the x-intercepts: (-8, 0), (-3, 0), (8, 0) Find the y-intercept: (0, -4) Name the intervals where the function is increasing: [-8, -6], [6, ∞ ] Name the intervals where the function is decreasing: [-6, 0], [4, 6] Name the interval where the function is flat: [0, 4]

9. Identify the features of the function. Name the maximum for the interval [-8, -5]: 7 Name the minimum for the interval [2, 8]: -8