How to Graph Any Function on the TI-84 Calculator

The graphing capability is what separates the TI-84 from a basic scientific calculator. Whether you need to visualize a parabola, analyze a sine wave, or find where two lines meet, the TI-84 makes it fast and visual. This guide walks you through graphing every major function type you'll encounter in high school and college math.

Follow along using our free online TI-84 calculator, switch to Graph mode and try each example as you read.

The Four Graphing Keys You Must Know

• Y=, Opens the function editor where you enter your equations.
• WINDOW, Controls the x and y range displayed on screen.
• ZOOM, Preset window configurations for quick setup.
• GRAPH, Draws the graph of all active Y= functions.
• TRACE, Moves a cursor along the graph to read coordinates.
• 2ND → TRACE (CALC), Advanced analysis tools (zeros, mins, maxes, intersections).

Step 1: Enter Your Function in Y=

Press Y= to open the function list. You can enter up to 10 functions (Y1 through Y0). The variable key is X,T,θ,n, always use this key for the independent variable, not the letter X from ALPHA. Each function gets its own color on the TI-84 Plus CE.

Clear any existing functions by moving to each Y= line and pressing CLEAR before entering new ones.

Step 2: Set Your Window

Press WINDOW to manually set the display range. Key settings:

• Xmin / Xmax, Left and right edges of the screen.
• Ymin / Ymax, Bottom and top edges of the screen.
• Xscl / Yscl, Spacing between tick marks on each axis.

The standard window (−10 to 10 on both axes) is the best starting point. Press ZOOM → 6: ZStandard to set it automatically.

Graphing Linear Functions (y = mx + b)

Linear functions are the simplest to graph. Example: graph y = 3x − 2.

1. Press Y=, then type 3X-2 next to Y1.
2. Press GRAPH (or ZOOM → 6 for standard window).
3. You see a straight line crossing the y-axis at −2 with slope 3.

To verify the slope, press TRACE and note how the y-value changes by 3 for every 1-unit increase in x.

Graphing Quadratic Functions (y = ax² + bx + c)

Example: graph y = x² − 4x + 3.

1. Press Y=, type X^2-4X+3 next to Y1.
2. Press GRAPH.
3. You see an upward-opening parabola.

Find the vertex: 2ND → TRACE → 3: minimum. The vertex is at (2, −1). Find the x-intercepts: 2ND → TRACE → 2: zero to get x = 1 and x = 3.

Graphing Trigonometric Functions

Before graphing trig functions, set the correct angle mode. Press MODE and select either Degree or Radian depending on your problem. Most pre-calculus graphing is done in radians.

Example: graph y = sin(x) in radian mode.

1. Press MODE → Radian → ENTER.
2. Press Y=, type sin(X) (use the SIN key, not letters).
3. Press ZOOM → 7: ZTrig to set the ideal window for trig functions (shows one full period clearly).
4. Press GRAPH.

To graph y = 2sin(3x + π/4), type 2*sin(3X+π/4). Remember: π is accessed via 2ND → ^.

Graphing Exponential Functions (y = aˣ)

Example: graph y = 2ˣ.

1. In Y1, type 2^X.
2. Press GRAPH with standard window.
3. You see rapid growth to the right and an asymptote approaching 0 on the left.

For y = eˣ, use the 2ND → LN (eˣ) key rather than typing E^X, to ensure the calculator uses Euler's number precisely.

Graphing Logarithmic Functions

Example: graph y = log(x) (base 10).

1. In Y1, type log(X) using the LOG key.
2. Adjust the window: set Xmin to −1, Xmax to 10, Ymin to −3, Ymax to 3.
3. The graph shows the characteristic logarithmic curve crossing (1, 0).

For natural log, use ln(X) with the LN key. For log base n, use the change-of-base formula: log(X)/log(n).

Graphing Absolute Value Functions

Example: graph y = |x − 3|.

1. Press Y=.
2. Press MATH → NUM → 1: abs(, then type X-3).
3. Press GRAPH. You see a V-shape with vertex at (3, 0).

Finding Intersections of Two Graphs

This is one of the most powerful graphing techniques. To find where two functions meet:

1. Enter the first function in Y1, the second in Y2.
2. Press GRAPH to see both curves.
3. Press 2ND → TRACE → 5: intersect.
4. Press ENTER to select curve 1, ENTER again for curve 2, move near the intersection, press ENTER for the guess.
5. The intersection coordinates are your solution.

Zoom Shortcuts You'll Use Every Day

• ZOOM 1: ZBox, Draw a box around an area to zoom in.
• ZOOM 2: Zoom In, Zoom in centered at the cursor.
• ZOOM 3: Zoom Out, Zoom out centered at the cursor.
• ZOOM 6: ZStandard, Reset to −10, 10 on both axes.
• ZOOM 7: ZTrig, Ideal window for trig functions.
• ZOOM 0: ZoomFit, Auto-fit y-range to show entire function.