Dawnbridge

TI-Nspire CX II field manual for IB Math

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19

Finding roots of a function

All courses

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.

Goal

Find every root of ​y=ln(x+2)−12x​−0.8.

1

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.

2

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.

Scratchpad
RAD
3

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.

Scratchpad
RAD
4

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.

Scratchpad
RAD
5

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.

Scratchpad
RAD
6

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.

Scratchpad
RAD
Result

The roots are approximately ​x≈0.278​ and ​x≈33.1.

Scratchpad
RAD

Your turn

Work each one on your calculator, then check the answer.

  1. 1

    Find all real roots of ​f(x)=x3−4x+1.

  2. 2

    Find all real roots of ​f(x)=ex−3x2.

  3. 3

    Find all real roots of ​f(x)=ln(x+3)−x2.