A function’s graph sometimes has details that are difficult to see. This is often because the graph’s details are too small or too large to see at the axes’ current scale. Figure 3.20.1 is a case in point. It shows the graph of $y = 2^x$ overlaid with the graph of $y = x^4$. Many high school textbooks state that exponential growth always overtakes polynomial growth, so in the case of Figure 3.20.1 there must be some number
N so that $2^x > x^4$ for all values of $x > N$. In other words, their graphs must have a third intersection point. But it is off the screen when the axes are scaled as in Figure 3.20.1. We need to rescale the axes to see the third intersection of the two graphs.
Figure 3.20.1. Using GC’s “zoom” buttons to change axes’ scales. Clicks
of the mouse show with black rings in the video. Clicks while holding
the “shift” key (“command” key on Mac) show in red rings.
What GC Does When It Zooms
When you click on one of GC’s zoom icon, it expands the visible axes (when zooming in) or it contracts the visible axes (when zooming out). Either way, it always keeps the origin in the same place, zooming in or out from it.
You also can rescale vertical and horizontal axes independently. Holding the
shift key (command key on Mac) when you click a zoom button re-scales only the vertical axis. Holding the alt key (option key on Mac) when you click a zoom button re-scales only the horizontal axis.
Zoom by “boxing”
Sometimes you’ll want to zoom in on a section of a graph instead of zooming the entire viewing area. Zoom in a section of a graph by holding the shift key as you click and drag to draw a box around the section you wish to expand.
Figure 3.20.2 shows a box being drawn around a section of a graph and what GC does after you release the mouse button.
Figure 3.20.2. Shift-click-drag to draw
a box. GC fills the viewing pane with the region you boxed.
How you draw a box will determine how you affect the proportions of your zoomed region. The animation in Figure 3.20.3 shows the sections of a graph being scaled differently according to how the box is drawn. If you want to stretch a section of a graph vertically, draw a short wide box. If you want to compress a section vertically, draw a tall narrow box. The function’s graph is unaffected. Only the scale of its display is affected.
Figure 3.20.3. Shift-click-drag to draw
a box. How you draw a box determines whether the scale will be stretched
or compressed vertically. The graph itself is unaffected. Only the scale
of its display is affected.
Exercise Set 3.20
Exercises 1-4: A section of each displayed graph is boxed. Predict how GC’s display of the graph will appear after releasing the mouse button. Then click the solution link to see how GC actually zoomed that section.