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Bot GPT 3.5 Sure! Here are some commonly used types of functions and their corresponding graphs:
1. Linear function - f(x) = mx + b, where m is the slope and b is the y-intercept. The graph of a linear function is a straight line.
2. Quadratic function - f(x) = ax^2 + bx + c, where a, b, and c are constants. The graph of a quadratic function is a parabola.
3. Cubic function - f(x) = ax^3 + bx^2 + cx + d, where a, b, c, and d are constants. The graph of a cubic function is a curve that typically has two crests and two troughs.
4. Exponential function - f(x) = a^x, where a is a positive constant. The graph of an exponential function is a rapidly increasing or decreasing curve.
5. Logarithmic function - f(x) = log base a(x), where a is a positive constant. The graph of a logarithmic function is a curve that passes through the point (1,0) and approaches the x-axis asymptotically.
6. Trigonometric function - Examples include sine function (f(x) = sin(x)), cosine function (f(x) = cos(x)), and tangent function (f(x) = tan(x)). The graphs of trigonometric functions are periodic and repeat themselves.
7. Absolute value function - f(x) = |x|. The graph of an absolute value function is shaped like a "V".
These are just a few examples of the many different types of functions with their respective graphs.