How to Check Answers to a Math Problem Using a Graphing Calculator

Step-by-Step Guide

1. 1

   Step 1: Input a function.

   Press Y= to input the function of X from your math equation.
   
   If the equation takes the format f(x)= , you may simply replace f(x) with Y.
   
   The X can be entered by pressing the X,T,θ{\displaystyle \theta }, n key.
   
   Press GRAPH to view the graph of this function. , Press WINDOW to alter the range of the XY-plane displayed on the GRAPH screen.
   
   This step may take some patience at first, but it gets much easier with practice.
   
   The ZOOM options "3.
   
   Zoom Out" and "0.
   
   ZoomFit" can be helpful, as well. , Press 2ND, then TRACE to access the "CALC" menu.
   
   This menu brings up a number of tools that can be used to make calculations based on the graph of the Y= function. , From the "CALCULATE" menu, choose one of the following by scrolling down with the arrow keys, then press ENTER: 1: value
   - calculate the value of Y at a specified value of X. 2: zero
   - calculate the value of X at which the Y-value is equal to zero (also called "zeros" or "roots" of the function).
   
   These coordinates, by definition, lie on the X-axis. 3: minimum
   - calculate the XY-coordinates of a local minimum of the graph (where a low point occurs). 4: maximum
   - calculate the XY-coordinates of a local maximum (a high point) of the graph. 5: intersect
   - used when plotting 2 or more graphs to calculate a point of intersection of 2 curves. 6: dy/dx
   - used in Calculus to determine the rate of change (or slope of the tangent) of a function curve at a specified value of X. 7: ∫{\displaystyle \int }f(x)dx
   - used in Calculus to determine the area between a function curve and the X-axis, between 2 specified values of X (called "bounds"). , Some of the options may require you to input more information.
   
   For example, selection of options
   2.
   -
   4. will bring up prompts for the user to input the "Left Bound?"
   
   then the "Right Bound?"
   
   and finally a "Guess?" This will set a region for the calculator to focus on, as more than one zero or min/max point may be present.
   
   Some of the options may not bring up a prompt at all.
   
   Simply input the specified value of X (which may be your calculated answer, if you are checking your work), then press ENTER. , In Calculus 2, you will be plotting 2-dimensional graphs using variables outside of X and Y.
   
   This section will show you how to set up your calculator to accommodate these alternative formats.
   
   Start by pressing MODE. , Scroll down to the term "Func," an abbreviation for "function of X."
   
   Press ENTER to select.
   
   Your calculator is now ready to graph in Parametric format.
   
   In this format, X and Y are dependent on the value T, time, and are independent of each other. , Press Y= to input your relevant functions of T.
   
   Now, the X, T, θ{\displaystyle \theta }, n key will input a T, instead of an X. , Follow Part 1, Step 3 to access the "CALCULATE" menu, once again.
   
   Now, you are able to choose from the following options: 1: value
   - calculate the XY coordinates at a specified value of T. 2: dy/dx
   - calculate the slope of the line tangent to the curve at a specified value of T. 3: dy/dt
   - calculate the rate at which Y-values are changing at a specified value of T. 4: dx/dt
   - calculate the rate at which X-values are changing at a specified of T. , Your calculator is now ready to graph in Polar form.
   
   In Polar graphing, the radius from the origin, r, is dependent on the angle in radians, θ{\displaystyle \theta }. *NOTE:
   If your calculator is in Degree mode, switch to Radian mode at this time. , Press Y= to input your relevant r(θ{\displaystyle \theta }) function.
   
   You may input θ{\displaystyle \theta } by pressing the X, T, θ{\displaystyle \theta }, n key. , Press 2ND, then TRACE to access the "CALCULATE" menu.
   
   You are now able to select one of the options listed below.
   
   In the picture example, π{\displaystyle \pi }/4 is entered as the value of θ{\displaystyle \theta } after selecting options 1: value. 1: value
   - calculate the XY coordinates at a specified value of θ{\displaystyle \theta }. 2: dy/dx
   - calculate the slope of the line tangent to the curve at a specified value of θ{\displaystyle \theta }. 3: dr/dθ{\displaystyle \theta }- calculate the rate at which r-values are changing at a specified value of θ{\displaystyle \theta }. , When working with statistics, we usually work with a list of compiled data.
   
   This section will show you how to input a list of data entries and access functions that will determine important statistical information.
   
   To get started, press the STAT key, then select "1:
   Edit..."
   
   Enter your data entries, in no particular order, down the column of list L1.
   
   Set your calculator back to "Func" mode (see Part 2, Steps
   1. and
   2.) and clear any existing functions on your Y= screen before moving on , You can plot your data several ways, but let's focus on two in detail.
   
   Press 2ND, then Y= to select STAT PLOT.
   
   Select "1:
   Plot 1" and set it to "On."
   
   Scroll Down to select an option for plot "Type." Select the top right bar graph to create a Histogram on your GRAPH screen.
   
   The screen will display that the values of L1 will be listed along the X-axis. , Press the WINDOW key.
   
   Select an Xmin and X max to fit the range of your data.
   
   In this example, the list contains 15 entries ranging from 47 to
   73.
   
   The Xscl selection will determine the column range of each Histogram bar.
   
   The Histogram will affix itself to the X-axis, so the Ymin should be set to zero.
   
   The Ymax is set to 5 in the picture shown. , Press GRAPH to view the Histogram.
   
   Press TRACE to establish a cursor on the GRAPH screen.
   
   Use the left and right arrow keys to move the cursor, which will define the range of the bar it lies on, as well as the number of entries represented by the bar. , Follow Step 3 to return to the Plot 1 settings.
   
   Under "Type," select the bottom center option to create Box-and-Whisker plot on your GRAPH screen.
   
   The Window view will remain the same. , Press GRAPH to view the Box-and-Whisker plot.
   
   Press TRACE to bring up the cursor, and use the left and right arrow keys to view the following values: minX
   - the lowest valued data entry Q1
   - the first quartile value (median of lower half of data) Med
   - the median of the data Q3
   - the third quartile value (median of upper half of data) maxX
   - the highest valued data entry , These values will be a critical component of any statistics introduction course.
   
   Press 2ND, then STAT to access the LIST menu. , Choose option
   3. for mean (the average data value),
   7. for standard deviation, and
   8. for variance. , Selection of any option listed in Step 10 will take you back to the home screen, where the user will enter the list that contains the data compilation.
   
   Press 2ND, then 1 to input L1, then press ENTER.
2. 2

   Step 2: Adjust your window view to see key features of the graph of the function.

3. 3

   Step 3: Access the "CALCULATE" menu.

4. 4

   Step 4: Select an option.

5. 5

   Step 5: Follow the prompts.

6. 6

   Step 6: Access the "MODE" menu.

7. 7

   Step 7: Highlight the "Func" option.

8. 8

   Step 8: Select the term "Par."

9. 9

   Step 9: Input a set of functions in Parametric form.

10. 10

    Step 10: Perform graph-based calculations in Parametric form.

11. 11

    Step 11: Repeat steps 1 and 2 from Part 2

12. 12

    Step 12: and select the term "Pol."

13. 13

    Step 13: Input a function in Polar form.

14. 14

    Step 14: Perform graph-based calculations in Polar form.

15. 15

    Step 15: Access the "STAT" menu.

16. 16

    Step 16: Compile a list of data.

17. 17

    Step 17: Plot your data.

18. 18

    Step 18: Make a Histogram.

19. 19

    Step 19: Adjust your calculator's Window view to fit your data entries.

20. 20

    Step 20: Find relevant information on your Histogram plot.

21. 21

    Step 21: Make a Box-and-Whisker plot.

22. 22

    Step 22: Find relevant information on your Box-and-Whisker plot.

23. 23

    Step 23: Access the "LIST" menu to determine mean

24. 24

    Step 24: variance

25. 25

    Step 25: and standard deviation.

26. 26

    Step 26: Scroll right to the "MATH" menu

27. 27

    Step 27: then select an option.

28. 28

    Step 28: Choose the appropriate list.

Detailed Guide

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