TI-Nspire CX II 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.
Open the Scratchpad's Graph view ( → B: Graph Scratchpad) and enter both functions. On f1(x)=, press then for the e^▯ template, type the exponent , then press to leave the template and type ; press . On f2(x)= type and press . To revisit either definition once you're out on the graph, returns the cursor to the entry line.
Frame the curves on the standard window: → 4: Window / Zoom → 5: Zoom – Standard. One crossing is visible near the right edge (around x ≈ 6), but the exponential climbs 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 → 4: Window / Zoom → 4: Zoom – Out, then and to put the zoom tool away. Each press zooms out by a factor of 2, so four presses take x from ±10 to ±160 and all three intersections sit on screen, clustered near the centre.
Tighten the window around just the crossings: → 4: Window / Zoom → 2: Zoom – Box. Touchpad to the upper-left of the cluster and press (or click the touchpad) to anchor the first corner. Touchpad 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. Read each one off: → 6: Analyze Graph → 4: Intersection. At lower bound? touchpad just left of a crossing and press ; at upper bound? touchpad just right of it and press . The crossing is labelled directly on the graph.
Repeat for the other two crossings. Each label stays on the graph, so all three intersections end up shown together.
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.