Dawnbridge

TI-84 Plus CE field manual for IB Math

Everyone · 13 of 45

13

Reading a graph: trace and zoom

All courses

Move a cursor along a plotted curve to read coordinates from it, and use the zoom menu to choose the viewing window deliberately.

Goal

Trace the graph of y=x32x+1 to read coordinates from it, and use the window to locate its vertical asymptote.

1

Trace moves a cursor along the curve. Graph the function on the standard window, then press . A cursor appears on the curve, and the bottom of the screen shows its X= and Y= coordinates. and move the cursor along the curve, and and switch between curves when more than one is plotted. The top-left corner names the function the cursor is on.

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X=1.363636364Y=-2.277777778
2

Trace moves in fixed steps, which sets its precision. Each press moves the cursor by the window width divided by 132: two columns of the 265-pixel graph area, listed as TraceStep on the screen. On the standard window that is 20÷1320.152, so one pass of trace pins an x-value down to about 0.15: roughly one significant figure. To read more precisely, shrink the window rather than pressing the arrow more carefully.

3

Typing a number jumps the cursor directly there. While tracing, type a value and press , and the cursor moves to that x-coordinate without walking to it.

4

The zoom menu, opened with , changes the window for you. The entries worth knowing:

  • 1: ZBox draws a rectangle: move to one corner, press , move to the opposite corner, press , and the window becomes that rectangle. In the screen below, the dashed box around the left branch becomes the new window.
  • 2: Zoom In and 3: Zoom Out quarter or quadruple the visible range about the cursor, by a factor of 4 each press.
  • 6: ZStandard resets the window to −10 to 10 on both axes.
  • 0: ZoomFit keeps the x-range and chooses a y-range that fits the curve, which corrects a graph that appears as a flat line along one edge.

For a window that a question specifies exactly, type it directly with instead.

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5

Now locate the vertical asymptote. Trace rightwards towards x=3: at x2.88 the readout shows y=−55.75, and one press later, at x3.03, it shows y=233. A jump from a large negative value to a large positive one within a single step means the asymptote lies between those two x-values.

6

Narrow the window by hand, not with a box. Near the asymptote the curve plunges far outside any small y-range, so a Zoom Box drawn there would contain no curve at all. Instead press and type the bracket into x while opening y wide: Xmin=2.95, Xmax=3.04, Ymin=-1000, Ymax=1000. Both branches stay on screen. Press again: the jump now happens between x2.9998 (y−30800) and x3.0005 (y15400), so one round has narrowed the bracket from about 0.15 to about 0.0007.

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7

One setting matters here. Press for FORMAT and turn Detect Asymptotes on. When it is off, the calculator draws a false steep line across the asymptote, and trace will report ordinary-looking coordinates along that line. Turning it on makes graphs draw slightly more slowly and removes the false line.

Result

The vertical asymptote is at x=3.00 to 3 s.f. To read any value from a graph more precisely, narrow the window and trace again.