Graphing Calculator

How to Use the Graphing Calculator

1. Type a function in the f(x) box using x as the variable.
2. Add more functions in g(x) and h(x) to compare them. Each has its own color.
3. Adjust the view with Zoom in, Zoom out, or by typing x min, x max, y min and y max.
4. Read the key points in the result panel: where each function crosses the x-axis and the y-axis.

Writing Functions the Calculator Understands

You want	Type
x squared	x^2
3 times x	3x or 3*x
Square root	sqrt(x)
Cube root	cbrt(x)
Sine, cosine, tangent (radians)	sin(x), cos(x), tan(x)
e to the x	exp(x) or e^x
Natural log	log(x)
Absolute value	abs(x)
Fractions	(x + 1)/(x - 2)

Use brackets generously. 1/2x is read as (1/2)·x. If you mean 1/(2x), type 1/(2x).

Reading a Graph: A Worked Example

Take the two default functions, f(x) = x² − 4 and g(x) = sin(x), on a window from −10 to 10.

• f(x) = x² − 4 is a parabola opening upwards. Setting x² − 4 = 0 gives x = ±2, so it crosses the x-axis at −2 and 2. At x = 0 it equals −4, its y-intercept and lowest point.
• g(x) = sin(x) is a wave between −1 and 1. It crosses the x-axis at every multiple of π, so between −10 and 10 the calculator lists −9.4248, −6.2832, −3.1416, 0, 3.1416, 6.2832 and 9.4248.

Where the two graphs cross, x² − 4 = sin(x). There’s no neat formula for that, but zooming in on the crossing points shows they are close to x ≈ −1.74 and x ≈ 2.19.

Choosing a Good Viewing Window

Start wide, then zoom

If you don’t know what a function looks like, start with −10 to 10 on both axes, then zoom in on the interesting part. Zoom in halves the window around its center; Zoom out doubles it.

Match the scale to the numbers

A function like 500x + 2000 needs a y range in the thousands. Set y min to −1000 and y max to 10000, and the line becomes visible instead of shooting off the top of the screen.

Trig functions use radians

sin, cos and tan expect radians, so one full wave of sin(x) is 2π ≈ 6.28 units wide. To work in degrees, type sin(x * pi / 180) and set the x range to −360 to 360.

Common Mistakes

• Forgetting the multiplication sign between brackets. (x+1)(x-1) works, but 2(x+1) and 2*(x+1) are safest.
• Using a variable other than x. The grapher only plots functions of x. Use the algebra calculator to solve equations in other variables.
• Expecting exact roots. Intercepts are numerical, to about four decimal places. For an exact answer such as (5 ± √13)/2, solve the equation in the algebra calculator.
• Looking for asymptotes as lines. Functions like 1/x jump at x = 0. The calculator breaks the line there rather than drawing a false vertical line.

To find the slope of a curve at any point, use the derivative calculator.