Wrapping up 1.3 Notes

Front

What is a function?

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

What are the characteristics of a linear function?

Back

A linear function has a constant rate of change and can be represented by the equation y = mx + b, where m is the slope and b is the y-intercept.

Front

What defines a quadratic function?

Back

A quadratic function is a polynomial function of degree 2, typically represented in the form y = ax^2 + bx + c, where a, b, and c are constants.

Front

How can you identify the maximum value of a quadratic function?

Back

The maximum value of a quadratic function occurs at the vertex of the parabola, which can be found using the formula x = -b/(2a) for the vertex's x-coordinate.

Front

What does it mean for a function to be increasing?

Back

A function is increasing on an interval if, for any two points x1 and x2 in that interval, if x1 < x2 then f(x1) < f(x2).

Front

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

Back

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

Front

What is the standard form of a quadratic function?

Back

The standard form of a quadratic function is y = ax^2 + bx + c.

Front

How do you determine the intervals where a function is increasing or decreasing?

Back

To determine the intervals where a function is increasing or decreasing, analyze the first derivative of the function; where the derivative is positive, the function is increasing, and where it is negative, the function is decreasing.

Front

What is the y-intercept of a function?

Back

The y-intercept of a function is the point where the graph of the function intersects the y-axis, which occurs when x = 0.

Front

What is the slope of a linear function?

Back

The slope of a linear function represents the rate of change of the function and is calculated as the change in y divided by the change in x (rise/run).