Module 14

14.1.2

New Section 14.1.2 Evaluating a Function with a Graphing Calculator Objective: Evaluating a Function with a Graphing Calculator If you need to evaluate the same function more than once with different input values, it may be more efficient to use a graphing calculator. There are several ways the graphing calculator can be used to evaluate a function. How to enter an expression: Remove 2nd expression from the example. Note Instructions in this section are for a TI 83/84 graphing calculator.

New Section 14.1.2 Evaluating a Function with a Graphing Calculator Objective: Evaluating a Function with a Graphing Calculator Evaluate (4x + 7)5x2 + 6x + 4 𝑥  find f(4) and f(-6) Notes Add to current content: The STO button assigns the given value to the indicated variable. Answer = 2415 Add ENTER to the end of this instruction.

New Section 14.1.2 Evaluating a Function with a Graphing Calculator Objective: Evaluating a Function with a Graphing Calculator Evaluate (4x + 7)5x2 + 6x + 4 𝑥  find f(4) and f(-6)

New Section 14.1.2 Evaluating a Function with a Graphing Calculator Objective: Evaluating a Function with a Graphing Calculator Evaluate (4x + 7)5x2 + 6x + 4 𝑥  find f(4) and f(-6) Use the and keys to search for the desired f(x). In this example, f(4) and f(-6) -10 for example This number indicates the increments for the table. For larger values larger increments of 10, 50 or 100 may be necessary to see required values. Note

14.1.2 Examples *For each example there should be at least two versions for each of the examples listed. In this way, Example 1 would have at least 6 versions. *Each example should contain a button for each method. Using STO Using Y = Using Table Add “How to Enter an Absolute Value” button to this example. See contents on next slide.

How to Enter Absolute Value Press Press in order to select NUM Press in order to select abs( Enter value or expression within | |. Math 1

14.2.2

14.2.2 Optional Tutorial: Adjusting the Graphing Window Based on the function to be viewed, it is at times necessary to adjust the graphing window. Press to view the current window settings. WINDOW If these standard settings are not present on the calculator, they can be reset by pressing . ZOOM 6

14.2.2 Optional Tutorial: Changing the Graphing Window At times it is necessary to adjust the MIN, MAX and SCL values in order to obtain a clearer view of the graph. A graph of y = |x + 15| will not be entirely visible in the standard viewing window. A view of the table of values, reveals that the window will need to be enlarged in order to view more points on the graph. Use the “+” to set the Tbl value to 5. This sets the increments of the table to 5. Next

14.2.2 Optional Tutorial: Changing the Graphing Window Change the window settings to accommodate a greater number of domain and range values. Review the following images to view the change in the graphing window. By changing the Max and Min values as well as the increments, the graphing window contains a more accurate picture of the graph. Remember: Press to view and adjust current settings. Press to reset the settings to Standard View. WINDOW ZOOM 6

14.2.2 Example 1 Although only one example is listed, the versions are of to be different types of equations. Students are to be presented with a function and are to be required to plot points on a graph in order to “draw” the solution. Versions of the following: f(x) = 2 3 𝑥 −5, 𝑓𝑖𝑛𝑑 f(3), f(1) f(x) = x2 – 2x + 3 f(x) = x3 – 2x2 + 3x -1 f(x) = |2x + 3| f(x) = 3(x + 5) – 4 f(x) = 𝑥+7

14.3.1

New Section 14.3.1 Objective: Solving Linear Equations with the Graphing Calculator Recall that you already know how to solve linear equations in one variable using symbolic methods. For example: 3(x-6) = 7 – 2x 3x – 18 = 7 – 2x 5x = 25 x = 5 These equations can also be solved using a graphing calculator, either numerically or graphically. These methods are important because they can also be used for non-linear equations which cannot be solved symbolically.

New Section 14.3.1 Objective: Solving Linear Equations with the Graphing Calculator Consider the linear equation in one variable: Write each side of the equation as a separate equation: This is a system of linear equations in two variables. On the graphing calculator, enter the first expression as Y1 and the second expression as Y2. 3(x-6)=7-2x y = 3(x – 6) y = 7 – 2x

New Section 14.3.1 Objective: Solving Linear Equations with the Graphing Calculator You can solve this system numerically by using the TABLE on your TI-83/84. Search the calculator table to find the value of x for which the two functions have equal y-values. Y1 = -3 and Y2 = -3, when x = 5, so the solution to the linear equation is x = 5.

New Section 14.3.1 Objective: Solving Linear Equations with the Graphing Calculator Next If the solution is not an integer, it may be easier to find the solution by graphing. Recall that the solution to a system is the intersection of the graphs. The y values will be the same at this point. The solution will be the x value at the point of intersection.

New Section 14.3.1 Objective: Solving Linear Equations with the Graphing Calculator To find the intersection: Press (INTERSECT) First Curve? This prompt asks if the indicated graph is involved in the intersection. Press to accept. Second Curve? This prompt asks if the indicated graph is involved in the intersection. Press to accept. Guess? In case there are multiple intersections, the calculator needs to know which intersection to evaluate. The Y value is not part of the solution. It indicates that the graphs are equal Y1 = Y2, at that particular point. Therefore the solution is x = 5. Note ENTER ENTER

Content for Note in section 14.3.1 In order to find the solution graphically, the intersection must be visible on the graph. It is necessary at times to change the Window settings in order to obtain a better view of the graph. Changing the Window settings, will NOT change the answer. These are the settings used for this graph.

14.3.1 Example 2 (table method) Note using the table method

14.3.1 Example 2 (graph method)