Evaluating Functions

Front

What is the definition of a function in mathematics?

Back

A function is a relation that assigns exactly one output for each input from a given set, known as the domain.

Front

What does it mean to evaluate a function at a specific point?

Back

Evaluating a function at a specific point means substituting the input value into the function's formula to find the corresponding output value.

Front

How do you evaluate a quadratic function?

Back

To evaluate a quadratic function, substitute the given x-value into the function's equation and perform the arithmetic operations according to 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 is the significance of the coefficient 'a' in a quadratic function?

Back

The coefficient 'a' determines the direction of the parabola (upward if a > 0, downward if a < 0) and affects the width of the parabola.

Front

What is the vertex of a quadratic function?

Back

The vertex is the highest or lowest point of the parabola, depending on the direction it opens, and can be found using the formula x = -b/(2a).

Front

What is the difference between linear and quadratic functions?

Back

Linear functions have a constant rate of change and graph as straight lines, while quadratic functions have a variable rate of change and graph as parabolas.

Front

How do you find the output of a linear function?

Back

To find the output of a linear function, substitute the input value into the function's equation and solve for the output.

Front

What is the formula for a linear function?

Back

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

Front

What is the process for evaluating a function with a negative input?

Back

To evaluate a function with a negative input, substitute the negative value into the function's equation and simplify as usual.