Casio fx-CG50 field manual for IB Math
Finding intersections
Plot two functions and read every intersection by zooming to standard, zooming out until the crossings fit, then drawing a Zoom Box around the cluster and using the calculator's intersect tool.
Find every intersection of y1=ex(x2−11x+30) and y2=(x−8)2.
From the MAIN MENU open Graph (icon 5). On Y1: press for the e^▯ template, type the exponent , then to leave the template and ; press . On Y2: type and press .
Frame the curves on the standard window: (V-Window) → (STANDRD) loads the ±10 window. Press to return to the editor, then (DRAW) to plot. Two crossings appear on the right (around x ≈ 5 and x ≈ 6), but the exponential rockets straight off the top before x = 1, so you can't tell from this view whether more intersections are hidden above the visible window.
Pull the camera back so the crossings come into view. Press (Zoom) → (OUT) to zoom out once, then repeat (Zoom) → (OUT) two more times. Each press multiplies the visible window by the Xfact/Yfact factors set in Zoom → (FACT), default 2. Three zooms expand the window to [-80, 80] × [-80, 80] and all three intersections are now on screen, packed near the centre.
Tighten the window around just the crossings: (Zoom) → (BOX). Use the d-pad to move the cursor to the upper-left of the cluster and press to anchor the first corner. Move to the lower-right and press again. The dashed marquee shows the region you've selected.
The window snaps to the box and the three crossings are clearly separated. Now read them off precisely: (G-Solv) → (INTSECT). The Casio solves all three intersections and steps through them in order from left to right; the screen shows one at a time, and you move between them with the / cursor.
The three intersections are approximately (0.876,50.7), (4.94,9.38), and (6.01,3.96).
Your turn
Work each one on your calculator, then check the answer.
- 1
Find all intersections of f(x)=ex/2 and g(x)=x2−3.
- 2
Find all intersections of f(x)=ln(x) and g(x)=0.02x2.
- 3
Find all intersections of f(x)=8sin(x) and g(x)=4x2−5.