Evaluating Functions (Equations & Graphs)

Front

What is the definition of a function?

Back

A function is a relation that assigns exactly one output value for each input value.

Front

How do you evaluate a function at a specific point?

Back

To evaluate a function at a specific point, substitute the input value into the function's equation and simplify.

Front

What is the general form of a quadratic function?

Back

The general form of a quadratic function is f(x) = ax² + bx + c, where a, b, and c are constants.

Front

What does the vertex of a parabola represent in a quadratic function?

Back

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

Front

How do you find the range of a quadratic function?

Back

The range of a quadratic function can be found by determining the vertex and the direction of the parabola (opening upwards or downwards).

Front

What is the significance of the coefficients in a quadratic function?

Back

The coefficient 'a' determines the direction and width of the parabola, while 'b' affects the position of the vertex, and 'c' represents the y-intercept.

Front

What is the y-intercept of a function?

Back

The y-intercept of a function is the point where the graph intersects the y-axis, found by evaluating the function at x = 0.

Front

How do you determine if a function is increasing or decreasing?

Back

A function is increasing where its derivative is positive and decreasing where its derivative is negative.

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.

Front

What is the difference between a linear function and a quadratic function?

Back

A linear function has a constant rate of change and is represented by a straight line, while a quadratic function has a variable rate of change and is represented by a parabola.