Is it Linear, Exponential or Quadratic

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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 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 represents growth or decay that accelerates over time.

Front

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) = ax^2 + bx + c, where a, b, and c are constants and a ≠ 0. Its graph is a parabola.

Front

How can you identify a linear function from a table of values?

Back

A linear function will have a constant rate of change between the x-values and y-values. This means that the difference in y-values divided by the difference in x-values will be the same for any two points.

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What does it mean for a function to exhibit exponential growth?

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Exponential growth occurs when the increase of a quantity is proportional to its current value, leading to rapid increases over time, often modeled by functions like f(x) = a * 3^x.

Front

What is the general shape of a quadratic function's graph?

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The graph of a quadratic function is a parabola, which can open upwards or downwards depending on the sign of the coefficient 'a' in the function f(x) = ax^2 + bx + c.

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What is the difference between linear and quadratic functions?

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Linear functions produce straight-line graphs and have a constant rate of change, while quadratic functions produce parabolic graphs and have a variable rate of change.

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What is an example of a real-world situation that can be modeled by a linear function?

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An example is a person receiving a fixed allowance increase each week, such as $1 more each week.

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What is an example of a real-world situation that can be modeled by an exponential function?

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An example is bacteria growth, where the population triples every day, representing exponential growth.

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What is the standard form of a linear equation?

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The standard form of a linear equation is Ax + By = C, where A, B, and C are integers, and A should be non-negative.