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

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 y-intercept of a function?

Back

The y-intercept is the value of the function when the input (x) is zero; it is the point where the graph intersects the y-axis.

Front

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

Back

To find the x-intercept, set the output of the function (f(x)) to zero and solve for the input (x).

Front

What is a quadratic function?

Back

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

Front

What is the vertex of a quadratic function?

Back

The vertex is the highest or lowest point of the parabola represented by the quadratic function, depending on the direction it opens.

Front

How do you determine the maximum or minimum value of a quadratic function?

Back

The maximum or minimum value occurs at the vertex of the parabola, which can be found using the formula x = -b/(2a) for the function f(x) = ax^2 + bx + c.

Front

What is the significance of the discriminant in a quadratic equation?

Back

The discriminant (b^2 - 4ac) determines the nature of the roots of the quadratic equation: if positive, there are two real roots; if zero, one real root; if negative, no real roots.