LAB 1: Graphing Calculator: Graphing a Function and Building a Table

New Concept

A graphing calculator can be used to analyze functions. The calculator can be used to graph the function as well as build tables of data.

What’s next

Next, you’ll master this tool by graphing a linear function, tracing its key points, and building a custom data table from the equation.

A graphing calculator can visualize functions. To graph a line like $y = 2x + 7$, you must first enter the equation into the Y= editor. Once entered, pressing the GRAPH button will display the function on a coordinate plane. The ZOOM button and ZStandard option ensure the graph is shown in a standard viewing window for proper analysis.

To graph $y = -3x + 5$, press Y=, enter -3X,T,θ,n + 5, and then press GRAPH.
To visualize $y = 0.5x - 2$, enter it into the Y= editor and press ZOOM then 6:ZStandard for a clear view.
For $y = x^2 - 4$, enter X,T,θ,n x² - 4 into the Y= editor and press GRAPH to see the parabola.

Think of the calculator as your personal artist! Just give it the instructions (the equation), and it will instantly draw the picture (the graph) for you. It's a super-fast way to visualize how an equation looks without having to plot a bunch of points by hand. See the line, understand the function, and let the calculator do the heavy lifting!

The TRACE feature allows you to move a cursor along a graphed function. As you move the cursor with the arrow keys, the calculator displays the corresponding $x$ and $y$ coordinates at the bottom of the screen. This is a practical way to find specific points on the line, such as the $x$-intercept (where $y=0$) and the $y$-intercept (where $x=0$).

For the graph of $y = -2x + 4$, press TRACE and use the arrow keys to find where $x=0$. The display will show $y=4$, the y-intercept.
On the graph of $y = x - 6$, press TRACE, type 6, and press ENTER. The cursor will jump to the point $(6, 0)$, the x-intercept.

Imagine you're a detective walking along the graphed line. The TRACE tool is your magnifying glass, showing the exact coordinates of every step. This is perfect for zeroing in on important clues like where the line crosses the axes—the x and y-intercepts. Just move the cursor or type an x-value to jump right to the spot!

A calculator can automatically generate a table of values for any function you've entered. By accessing the TABLE feature, you can see a list of $x$-values in the first column and their corresponding $y$-values in the second. You can scroll through this table using the arrow keys to explore different points on the function's graph without tracing.

For the function $y = 4x - 6$, press 2nd + GRAPH to see a table showing points like $(0, -6)$, $(1, -2)$, and $(2, 2)$.
To view the table for $y = x + 10$, you can quickly find the value of $y$ when $x=50$ by scrolling down the list.
For $y = -5x+3$, access the table to confirm that the point $(2, -7)$ is on the line.

Why do all the math yourself when your calculator can be your personal assistant? It can generate a perfect list of coordinates that lie on your line. This is incredibly useful for checking your homework, finding specific points, or just seeing how the y-value changes as the x-value increases step-by-step. It's organized data on demand!

The table's settings can be customized through the TBLSET menu. The TblStart option sets the initial $x$-value displayed in the table. The ΔTbl option, or delta table, defines the increment between consecutive $x$-values. This allows you to create tables with specific starting points and step sizes, such as listing only odd numbers or decimal values.

For $y = -3x + 8$, go to TBLSET, set TblStart=1 and ΔTbl=2 to create a table showing values for odd-numbered $x$.
To create a table for $y=4x-6$ with decimal steps, go to TBLSET and set ΔTbl=0.5 to see values for $x=0, 0.5, 1, 1.5$, etc.
To see values for $y = 10x$ starting at $x=20$, set TblStart=20 and ΔTbl=10.

You're the director of this math movie! Don't like where the table starts or how it's counting? Jump into the TBLSET menu to take control. You can tell it to start at 100, count by fives, or even show decimal steps. This customization lets you focus on the exact part of the function you're most interested in exploring.