Graphing techniques
Check the graph and its symmetries · Diagrams · Complete reading
Calculator mode and fraction entries
MODE: select FUNCTION with arrows and ENTER
- MATHPRINT CLASSIC
- NORMAL SCI ENG
- FLOAT 0 1 2 3 4 5 6 7 8 9
- RADIAN DEGREE
- [FUNCTION] PARAMETRIC POLAR SEQ
- THICK DOT-THICK THIN DOT-THIN
- SEQUENTIAL SIMUL
- REAL a+bi re^(θi)
- FULL HORIZONTAL GRAPH-TABLE
- FRACTION TYPE: n/d Un/d
- ANSWERS: AUTO DEC FRAC-APPROX
- GOTO 2ND FORMAT GRAPH: NO YES
- STAT DIAGNOSTICS: OFF ON
- STAT WIZARDS: ON OFF
The source highlights FUNCTION; its complete screen is in the evidence.
Fraction alternative: ALPHA → Y=
- FRAC menu: 1:n/d 2:Un/d
- 3: n/d ↔ Un/d 4: F ↔ D
- Select 1:n/d; numerator 1, denominator X gives Y₁ = 1/X.
- Use denominator X² for Y₁ = 1/X².
Teacher guidance: use TI-SmartView to introduce graphing settings.
Menu reconstruction retains source options; the date/clock is not a setting task.
Basic curves: square, cube and square root
y = x²
Y₁ = X²
Y= → X,T,θ,n → x² → GRAPH
Domain: All real inputs.
Parabola; vertex (0, 0).
y = x³
Y₁ = X^3
Y= → X,T,θ,n → ^ → 3 → GRAPH
Domain: All real inputs.
Near (0,0): ZOOM → 2 → ENTER (Zoom In).
y = √x
Y₁ = √(X)
Y= → 2nd → x² → X,T,θ,n → GRAPH
Domain: x ≥ 0.
Real inputs x ≥ 0; the curve begins at the origin.
Input/result reconstructions; viewing windows chosen for clear mathematical shape.
Basic curves: reciprocals and cube root
y = 1/x
Y₁ = 1/X
Y= → 1 → ÷ → X,T,θ,n → GRAPH
Domain: x ≠ 0.
Two branches. Alternative entry: ALPHA → Y= (fraction template).
y = 1/x²
Y₁ = 1/X²
Y= → 1 → ÷ → X,T,θ,n → x² → GRAPH
Domain: x ≠ 0.
Both branches positive; the input 0 is excluded.
y = ∛x
Y₁ = ∛(X)
Y= → MATH → 4 → X,T,θ,n → GRAPH
Domain: All real inputs.
Real cube root: negative inputs give negative outputs.
Input/result reconstructions; viewing windows chosen for clear mathematical shape.
Basic curves: exponential and logarithm
y = eˣ
Y₁ = e^(X)
Y= → 2nd → LN → X,T,θ,n → GRAPH
Domain: All real inputs.
Increasing; y-intercept 1 and left-end asymptote y = 0.
y = e⁻ˣ
Y₁ = e^(−X)
Y= → 2nd → LN → (−) → X,T,θ,n → GRAPH
Domain: All real inputs.
Use the negation key (−); decreasing, with y-intercept 1.
y = ln x
Y₁ = ln(X)
Y= → LN → X,T,θ,n → GRAPH
Domain: x > 0.
Real inputs x > 0; x-intercept 1; vertical asymptote x = 0.
Input/result reconstructions; viewing windows chosen for clear mathematical shape.
Read a logarithm beyond the sampled screen
Calculator notes
y = ln x: a finite sampled screen is not the whole curve
6:ZStandard: coarse positive-input samples in a −10..10 window
Analytical shape: x > 0, y → −∞ as x → 0⁺; zero at x = 1.
Use zoom options to reveal features, then justify them analytically.
Source ZOOM menu (visible rows):
- 2:Zoom In 3:Zoom Out 4:ZDecimal
- 5:ZSquare 6:ZStandard 7:ZTrig
- 8:ZInteger 9:ZoomStat 0:ZoomFit
Cartesian diagrams show behaviour and relationships between variables.
Use conventions such as dotted asymptotes to identify the important features.
Sampling illustration, not an emulation of a specific calculator display.