EVALUATING FUNCTIONS

Front

What is a function in mathematics?

Back

A function is a relation between a set of inputs and a set of possible outputs where each input is related to exactly one output.

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How do you evaluate a function at a given point?

Back

To evaluate a function at a given point, substitute the input value into the function's equation and simplify to find the output.

Front

What does it mean for a function to be linear?

Back

A linear function is a function that can be graphically represented as a straight line, characterized by the equation y = mx + b, where m is the slope and b is the y-intercept.

Front

What is the difference between a function and a relation?

Back

A function is a specific type of relation where each input is associated with exactly one output, while a relation can have multiple outputs for a single input.

Front

What is the domain of a function?

Back

The domain of a function is the set of all possible input values (x-values) for which the function is defined.

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What is the range of a function?

Back

The range of a function is the set of all possible output values (y-values) that the function can produce.

Front

What is a quadratic function?

Back

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

Front

How do you find the x-intercepts of a function?

Back

To find the x-intercepts of a function, set the function equal to zero and solve for x.

Front

What is a piecewise function?

Back

A piecewise function is a function that is defined by different expressions or formulas for different intervals of the input variable.

Front

What is the significance of the slope in a linear function?

Back

The slope of a linear function indicates the rate of change of the function; it represents how much the output value changes for a unit change in the input value.