LAB 4: Graphing Calculator: Changing the Line and Window of a Graph

New Concept

The viewing window of the graphing calculator can be adjusted to best display a graph.

Why it matters

Algebra is the language of relationships, and graphs are their visual stories. Mastering the viewing window is like learning to focus a microscope; it allows you to zoom in on critical details and uncover solutions hidden in the data.

What’s next

Next, you’ll apply this by centering graphs, zooming in on key features, and changing line styles to represent inequalities.

Property

The viewing window of the graphing calculator can be adjusted to best display a graph by manually setting the Xmin, Xmax, Ymin, and Ymax values, or by using automated features like Zoom In, Zoom Out, and ZStandard.

To center the graph of $y = |2x - 3| + 1$ on its vertex at $(1.5, 1)$, set Xmin to $-8.5$ and Xmax to $11.5$.
To view a graph from $-20$ to $20$ on both axes, set Xmin = -20, Xmax = 20, Ymin = -20, and Ymax = 20$. Press ZOOM and select 6:ZStandard` to quickly reset the view to the default $-10$ to $10$ range.

Think of your calculator's screen as a camera's viewfinder. You can manually adjust the frame by setting the WINDOW values to perfectly center your shot on a key feature, like the vertex of a parabola. Or, if you are feeling adventurous, use the ZOOM buttons for a dramatic close-up or a wide-angle view. It is all about getting the best picture!

Property

A graphing calculator can be used to change the style of a line. By highlighting the line symbol to the left of an equation in the Y= editor and pressing ENTER, you can cycle through thick, less-than, greater-than, path, animate, and dot styles.

To make the graph of $y = 2x - 3$ bold, select the thick-line symbol in the Y= editor.
To graph the inequality $y \leq 2x - 3$, select the less-than-line symbol in the Y= editor.
To graph a step function as a series of points, use the dot tool to show it is not continuous.

Why settle for a plain, boring line when your graph can have personality? In the Y= menu, you can transform your line into a bold, thick statement, or use shading to represent inequalities. You can even create an animated path or a series of dots for more complex functions. It is like having a whole art kit for your equations!

Property

To graph an inequality such as $y \geq f(x)$ or $y \leq f(x)$, enter the function $f(x)$ into the Y= editor and change the line style to the 'greater-than' (shading above) or 'less-than' (shading below) symbol.

To graph $y \geq 5 - x$, enter $y = 5 - x$ and change the line style to the 'greater-than' symbol.
To visualize the solution to $y \leq x^2$, enter $y = x^2$ and change the line style to the 'less-than' symbol.

Graphing an inequality is like drawing a boundary and then shading in all the possible solutions. Your calculator does the heavy lifting! Just enter the boundary equation, then select the 'greater-than' symbol to shade above the line or the 'less-than' symbol to shade below it. It visually shows every single point that makes the inequality true.