Graphing Calculator Guide

Basic Functions

• Linear Functions: y = mx + b (where m is the slope and b is the y-intercept)
• Quadratic Functions: y = ax² + bx + c
• Cubic Functions: y = ax³ + bx² + cx + d
• Absolute Value: y = |x|
• Square Root: y = √x
• Reciprocal: y = 1/x

Trigonometric Functions

• Sine: y = sin(x)
• Cosine: y = cos(x)
• Tangent: y = tan(x)
• Secant: y = sec(x) or y = 1/cos(x)
• Cosecant: y = csc(x) or y = 1/sin(x)
• Cotangent: y = cot(x) or y = 1/tan(x)

Exponential and Logarithmic Functions

• Exponential: y = e^x
• Natural Logarithm: y = ln(x)
• Base-10 Logarithm: y = log(x)
• General Exponential: y = a^x (where a is a positive constant)

Conic Sections

• Circle: (x-h)² + (y-k)² = r² (center at (h,k) with radius r)
• Ellipse: (x-h)²/a² + (y-k)²/b² = 1
• Hyperbola: (x-h)²/a² - (y-k)²/b² = 1 or (y-k)²/a² - (x-h)²/b² = 1
• Parabola: y = a(x-h)² + k (vertex at (h,k))

Inequalities

• Linear Inequality: y > mx + b or y < mx + b
• Quadratic Inequality: y > ax² + bx + c or y < ax² + bx + c
• Region Bounded by Multiple Inequalities: Enter each inequality separately

Tips for Using the Calculator

• Use the mouse to pan the graph by clicking and dragging
• Zoom in and out using the scroll wheel or the zoom buttons
• Click on a point on the graph to see its coordinates
• Use parentheses to group expressions: (x+1)²
• For piecewise functions, use curly braces: y = {x>0: x, x≤0: -x}
• For implicit equations, simply enter the equation: x² + y² = 9