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.

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 equation and simplify.

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 parabola represent in a quadratic function?

Back

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

Front

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

Back

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

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 changes for a unit change in the input.

Front

How can you determine the number of solutions to a quadratic equation?

Back

The number of solutions to a quadratic equation can be determined using the discriminant (b^2 - 4ac). If the discriminant is positive, there are two solutions; if zero, one solution; if negative, no real solutions.

Front

What is a linear function?

Back

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

Front

How do you interpret the meaning of a function in a real-world context?

Back

Interpreting a function in a real-world context involves understanding what the variables represent and how changes in one variable affect another.

Front

What is the difference between independent and dependent variables in a function?

Back

The independent variable is the input of the function (often x), while the dependent variable is the output (often y) that depends on the value of the independent variable.