TI-Nspire CX II field manual for IB Math
Finding roots of a function
Plot a function, widen the x-window until every x-intercept is on screen, then use the calculator's root / zero tool to read each solution.
Find every root of y=ln(x+2)−12x−0.8.
Open the Scratchpad's Graph view ( → B: Graph Scratchpad) and enter the function on f1(x)=. Press then for the ln template; type ; press to leave the template, then type . Press to register the graph.
Start on the standard window: → 4: Window/Zoom → 5: Zoom-Standard. One root is visible near x≈0.278, but the graph is still above the x-axis at the right edge of the screen, so this view is too narrow to rule out another root farther right.
Widen the view to check the right side: → 4: Window/Zoom → 4: Zoom-Out, then press twice. The Nspire's Zoom-Out uses a fixed factor of 2, so x expands [-10,10] → [-20,20] → [-40,40], wide enough to reveal the second crossing near x≈33.1. The y-range scales with it, squashing the curve against the x-axis.
Crop back in with a box: → 4: Window/Zoom → 2: Zoom-Box. Click above-left of the curve's strip to anchor the first corner, then move below-right (keeping both crossings inside the marquee) and click again. The window snaps to the box, keeping the full x-coverage with a readable y-scale.
Read off the near root with → 6: Analyze Graph → 1: Zero. At lower bound? move just left of the crossing and press ; at upper bound? move just right and press . The located zero appears with its coordinates.
Repeat Analyze Graph → 1: Zero for the second root, the crossing on the right side of the screen. Bracket it the same way: lower bound just left of the crossing, then upper bound just right.
The roots are approximately x≈0.278 and x≈33.1.
Your turn
Work each one on your calculator, then check the answer.
- 1
Find all real roots of f(x)=x3−4x+1.
- 2
Find all real roots of f(x)=ex−3x2.
- 3
Find all real roots of f(x)=ln(x+3)−x2.