Function Families

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What is a Linear Function?

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A linear function is a function that can be graphically represented in the Cartesian plane 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 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. It shows rapid growth or decay.

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What is a Quadratic Function?

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

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What is an Absolute Value Function?

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An absolute value function is a function that returns the non-negative value of a number. It is defined as f(x) = |x|, which means the distance of x from 0 on the number line.

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How do you identify a Linear Function from its graph?

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A linear function's graph is a straight line. It has a constant slope and does not curve.

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How do you identify an Exponential Function from its graph?

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An exponential function's graph shows rapid growth or decay. It curves upwards for growth and downwards for decay, never touching the x-axis.

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How do you identify a Quadratic Function from its graph?

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A quadratic function's graph is a parabola, which can open upwards or downwards. It has a vertex and may have zero, one, or two x-intercepts.

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How do you identify an Absolute Value Function from its graph?

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An absolute value function's graph forms a 'V' shape, with the vertex at the point where the function equals zero.

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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 point where the graph intersects the y-axis, representing the value of f(x) when x = 0.