Evaluating Functions

Front

What is the definition of 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.

Front

How do you evaluate a function at a specific point?

Back

To evaluate a function at a specific point, substitute the value of the variable into the function's expression and simplify.

Front

What is the formula for a linear function?

Back

A linear function can be expressed in the form f(x) = mx + b, where m is the slope and b is the y-intercept.

Front

What does the slope of a linear function represent?

Back

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

Front

What is the significance of the y-intercept in a linear function?

Back

The y-intercept is the point where the graph of the function crosses the y-axis, representing the output value when the input is zero.

Front

How do you evaluate a quadratic function?

Back

To evaluate a quadratic function, substitute the value of the variable into the quadratic expression and simplify, following the order of operations.

Front

What is the standard form of a quadratic function?

Back

The standard form of a quadratic function is f(x) = ax^2 + bx + c, where a, b, and c are constants.

Front

What does the vertex of a quadratic function represent?

Back

The vertex of a quadratic function represents the maximum or minimum point of the graph, depending on the direction of the parabola.

Front

How do you find the value of a function at a negative input?

Back

To find the value of a function at a negative input, substitute the negative value into the function's expression and simplify.

Front

What is the difference between even and odd functions?

Back

An even function satisfies f(-x) = f(x) for all x, while an odd function satisfies f(-x) = -f(x) for all x.