Types of Functions

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What is a Linear Function?

Back

A linear function is a function that can be graphically represented as a straight line. It has the form f(x) = mx + b, where m is the slope and b is the y-intercept.

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What is a Quadratic Function?

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A quadratic function is a polynomial function of degree 2, typically in the form f(x) = ax² + bx + c, where a, b, and c are constants and a ≠ 0. Its graph is a parabola.

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What is an Exponential Function?

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An exponential function is a mathematical function of the form f(x) = a * b^x, where a is a constant, b is the base (a positive real number), and x is the exponent. Its graph shows rapid growth or decay.

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What does it mean for a relation to be 'Not a Function'?

Back

A relation is 'not a function' if it does not pass the vertical line test, meaning that for at least one input, there are multiple outputs.

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What is the general form of a Linear Function?

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The general form of a linear function is f(x) = mx + b, where m is the slope and b is the y-intercept.

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How can you identify a Quadratic Function from its graph?

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A quadratic function can be identified by its U-shaped graph (parabola) that opens upwards or downwards.

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What is the standard form of a Quadratic Function?

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The standard form of a quadratic function is f(x) = a(x - h)² + k, where (h, k) is the vertex of the parabola.

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What is the difference between Linear and Exponential Functions?

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Linear functions have a constant rate of change, while exponential functions have a variable rate of change that increases or decreases rapidly.

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What is the slope in a Linear Function?

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The slope (m) in a linear function represents the rate of change of the function; it indicates how much y changes for a unit change in x.

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What is the y-intercept in a Linear Function?

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The y-intercept (b) in a linear function is the value of y when x = 0; it is the point where the line crosses the y-axis.