WinPlot Tutorial Mr. R. Long Centennial Secondary School Hastings and Prince Edward DSB

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Morgan Floyd
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of pay: 1. Company A offers $11 per hour plus a flat fee of $150 every week 2.

1 WinPlot Tutorial Mr. R. Long Centennial Secondary School Hastings and Prince Edward DSB SCENARIO: You are considering two different summer job offers and need to make a decision about which one will be best for you in terms of pay: 1. Company A offers $11 per hour plus a flat fee of $150 every week 2. Company B offers $15 per hour plus a flat fee of $70 every week (but this company is willing to negotiate) You are going to use WinPlot graphing software to analyze these job offers by looking at Graphical mathematical models. STEP 1: Determine the equation for each offer. Let y = Pay and x = number of hours (do not write in the duotangs). Write the equations on the answer sheet for Step 1. STEP 2: Starting WinPlot. After you click on WinPlot you will see the following introductory WinPlot screen. By clicking on Window you will be presented with the following two plotting options: x Select 2-dim. This allows you to create 2-dimensional graphs in the x, y plane. y STEP 3: SETTING SCALES. As with any graph the next step is to set the scale. This is done in WinPlot by selecting the View menu bar then selecting View. Select set corners and enter in appropriate ranges for x (left to right) and y (down to up) Hints: 1. x number of hours each week (what sort of range in hours do people work each week) 2. y pay each week (take the maximum number of hours and use the equation to figure out the maximum pay) 3. Go a little lower than the minimum and a little higher than the maximum. The window to the right shows one suitable choice for. Answer the question on the answer sheet for Step 3.

STEP 4: PLOTTING EQUATIONS. Plot the equation for Company A. Select Equa from the menu bar then select Explicit. Enter in the equation for Company A.

Your inventory should already be on but if you need it select Equa and then Inventory. Click on equa to show the equation right on the graph. Notice that the equation is the same colour as the graph.

scale: Check this if you want to see the scale (you always will) places: Refers to the number of decimal places in the scale.

2 STEP 4: PLOTTING EQUATIONS. Plot the equation for Company A. Select Equa from the menu bar then select Explicit. Enter in the equation for Company A. Make your line have pen width = 2 (it will be thicker) then change the color to red. STEP 5:THE INVENTORY BOX. Label the equation on the graph using the Inventory. Your inventory should already be on but if you need it select Equa and then Inventory. Click on equa to show the equation right on the graph. Notice that the equation is the same colour as the graph. STEP 6: SCALE ON AXIS. Set up the axis scale properly by selecting View and then Grid. interval: Refers to what x and y go up by. scale: Check this if you want to see the scale (you always will) places: Refers to the number of decimal places in the scale. freq: Refers to the frequency of the scale (freq = 1 means scale shown on every line, freq = 2 means scale shown on every other line). pi: only select this if you are Grade 11 U or Grade 11 M and you are working on trig functions. mark scale on: If you are working on applied or real-life math (mathematical modeling - like this question) select border but if you are working on pure math (e.g. exploring parallel and perpendicular lines) then select axes. Answer the question on the answer sheet for Step 6. Winplot Tutorial Page 2 of 9

STEP 7: AXIS LABELS. To label the axis select View from the menu bar then Axes and finally Labels. Label each axis with a variable and units. STEP 8: THE SLIDER.

This is the same as Trace on the graphing calculator. Move the slider (denoted by the red x ) along the graph with your mouse. To get an exact value type in x = 0, 10, 20, 30 and 40 hours.

Your inventory should already be on but if you need it then select Equa and then Inventory. Click on table to show the table. Once the table is opened select Params.

3 STEP 7: AXIS LABELS. To label the axis select View from the menu bar then Axes and finally Labels. Label each axis with a variable and units. STEP 8: THE SLIDER. Determine how much you would earn at 0 hours, 10 hours, 20 hours, 30 hours and 40 hours and how many hours it would take to earn $600. Select One from the menu bar then Slider. This is the same as Trace on the graphing calculator. Move the slider (denoted by the red x ) along the graph with your mouse. To get an exact value type in x = 0, 10, 20, 30 and 40 hours. Answer the question on the answer sheet for Step 8. STEP 9: TABLES. To answer the same question you can create a table on the INVENTORY BOX. Your inventory should already be on but if you need it then select Equa and then Inventory. Click on table to show the table. Once the table is opened select Params. Each table is created for values of x from the low value to the high value or in this case from 0 hours to 50 hours. The number of steps refers to how many steps are taken to go from the low to the high. Answer the question on the answer sheet for Step 9. STEP 10: ANIMATE. If you go back to STEP 1, Company B offered $15 per hour plus a flat fee of $70 every week but was willing to negotiate. This means that the rate/slope and initial value/yintercept can change (they are variable ). Instead of putting in the equation y = 15x + 70 we will enter in the equation y = mx + b (m is the rate and b is the initial value). Select Equa and then EXPLICIT and finally key in mx + b. Winplot Tutorial Page 3 of 9

You must set a left limit (Set L) and a right limit (Set R) on the animate boxes shown below.

4 We can vary m and b on the graph by animating them. Select Anim then m as shown in the screen capture below. Repeat for b. The next part is determining the range of values over which m will be varied. m = rate Vary from $10 per hour to $20 per hour. You must set a left limit (Set L) and a right limit (Set R) on the animate boxes shown below. The Set L and Set R buttons refer to the minimum and maximum values of the variable (in this case m). 1. For the minimum enter 10 then click on Set L. 2. For the maximum enter 20 then click on Set R. Do the same for b or initial value/y-intercept setting. Vary b from $0 to $100 using the same method. Winplot Tutorial Page 4 of 9

Animate m by moving the scroll bar from left to right between $10 and $20 per hour. You will be answering questions about the effect on the graph when you do this.

5 Animate m by moving the scroll bar from left to right between $10 and $20 per hour. You will be answering questions about the effect on the graph when you do this. Animate b by moving the scroll bar from left to right between $ 0 and $100. You will be answering questions about the effect on the graph when you do this. Answer the questions on the answer sheet for Step 10 STEP 11: SOLVING EQUATIONS (INTERSECTION OF LINES OR CURVES) Set m = $15/hr and b = $70 on the animate scroll bars to start. In order to decide which offer you will accept (Company A or Company B) you need to determine who pays the best. Finding out the Meeting point or point intersection of the two lines can do this. Select Two then Meeting to find the point of intersection. Make sure that you select the two lines of interest and record the point. In this case the point of intersection is (20 hours, $370). Answer the questions for Step 11 on the answer sheet. Winplot Tutorial Page 5 of 9

EXTENSIONS 1. STANDARD FORM (e.g. Ax + By + C=0) To graph equations in standard form enter in the equations using Equa from the menu bar then selecting y = f(x).

Next the grid will have to redone and the scale placed on the axis not the border. This windows for this are provided below.

Set Window Step 3: Set Grid ***Notice that none of the operations available to y=f(x) form are available (e.g. slider, meeting etc.) in standard form. 2.

6 EXTENSIONS 1. STANDARD FORM (e.g. Ax + By + C=0) To graph equations in standard form enter in the equations using Equa from the menu bar then selecting y = f(x). Graph the line 4x + 3y-12 = 0 using this method. You will need to change the scale. Do this by selecting View then View and setting out the window. Next the grid will have to redone and the scale placed on the axis not the border. This windows for this are provided below. Step 1: Standard Form Step 2: Set Window Step 3: Set Grid ***Notice that none of the operations available to y=f(x) form are available (e.g. slider, meeting etc.) in standard form. 2. ZEROS If we made the assumption that water put into a freezer at an initial temperature of 15º C decreased at the rate of 5º C per hour the equation relating Temperature (y) and time (x) would be y = -5x Question: Determine, graphically, when the water starts to freeze. In other words determine when y is equal to zero. This is called the root or zero of the equation. Method: Set the window and scales, enter the equation then select One followed by Zero. The box showing up will be as follows: In other words the water will start to freeze after 3 hours. Winplot Tutorial Page 6 of 9

7 3. EXTREME (MAXIMUMS AND MINIMUMS) Question: Determine, graphically, the minimum of y = x² - 2x +3. minimum/maximum or critical values of a function. This is called the Method: Set the window and scales, enter the equation (x² entered as x^2) then select One followed by Extreme. The box showing up will be as follows: ***TEXT To write text on the screen select Btns then Text then right click over where you want to enter the text. Type it in. 4. PIECEWISE FUNCTIONS Question: You make $10 per hour for the first 40 hours then time and a half for overtime pay after 40 hours. In other words you make $15 per hour after 40 hours. Method: The regular pay equation valid up to 40 hours would be y = 10x and the overtime pay equation, valid after 40 hours, would be y = 15(x-40) (do some review to find equations of lines if necessary). After setting the window and scales enter the piecewise equation in the form: joinx(f c,g) where f is the first function (f = 10x), c is the right x limit on where f is valid, g is the next function valid to the right of x = c. In this specific case the function would be: y = joinx(10x 40,15(x-40) + 400). Notice the change of slope at x = 40 Select View then turn off Connect Dots when working with piecewise functions. Winplot Tutorial Page 7 of 9

8 WinPlot Tutorial Answer Sheet Name: STEP 1: Company A: y = Company B: y = STEP 3: Consider the equation y = 7x relating dog years (y) and human years (x). If you wanted to graph dog years versus 0 to 10 human years, what would your View window look like? Fill in the window to the right. Show any work below. STEP 4: Draw a rough sketch of the WinPlot graph in the box below. Identify the initial value/y-int and rate/slope triangle. STEP 6: Write down your scale on the y-axis (e.g. starts at zero and goes up by ). Go back to the Grid box and enter in freq = 2 for y. What happened to the scale of your graph? Now it starts at zero and goes up by. Why is this? Explain. STEP 8: Use the slider to determine the pay if you work. 0 hrs =, 10 hrs = 20 hrs =, 30 hrs =, 40 hrs = Number of hours to earn pay of $600.00: Explain how you used to slider to do this. Winplot Tutorial Page 8 of 9

9 STEP 9: 1. Write down what your table looks like below. Complete differences for x and y. x ($) y (hrs) 2. Why did setting num steps = 5 result in x values of 0, 10, 20, 30, 40 and 50 (in other words going up by 10)? 3. If you wanted the table to go up by ones (e.g. 0, 1, 2, 3, 4, 5 ) what would you num steps to. Explain. STEP 10: 1. What happened to the graph as you varied m from $10 per hour to $20 per hour? Be specific. Does this make sense? Explain. 2. What happened to the graph as you varied b from $0 to $100? Be specific. Does this make sense? Explain. STEP 11: 1. What does the point of intersection mean in real-life related to this problem? Explain. 2. Say you expect to work about 30 hours per week. Use the graph to determine which company you would want to work. Explain giving specific evidence. Winplot Tutorial Page 9 of 9

September 08, Graph y 2 =x. How? Is it a function? Function?

September 08, Graph y 2 =x. How? Is it a function? Function? Graph y 2 =x How? Is it a function? Function? Section 1.3 Graphs of Functions Objective: Analyze the graphs of functions. Important Vocabulary Graph of a function The collection of ordered pairs ( x, f(x))