Identifying Function Types and Contexts

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 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 range of a function?

Back

The range of a function is the set of all possible output values (y-values) that the function can produce.

Front

What does the y-intercept of a function represent?

Back

The y-intercept is the point where the graph of the function crosses the y-axis, representing the output value when the input is zero.

Front

How do you find the y-intercept of a function f(x)?

Back

To find the y-intercept, substitute x = 0 into the function and solve for f(0).

Front

What is a quadratic function?

Back

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

Front

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

Back

The vertex is the highest or lowest point of the parabola, depending on whether it opens upwards or downwards.

Front

What is the significance of the x-intercepts of a function?

Back

The x-intercepts are the points where the graph crosses the x-axis, representing the input values for which the output is zero.

Front

What is a linear function?

Back

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

Front

What is the slope of a line?

Back

The slope of a line is a measure of its steepness, calculated as the change in y divided by the change in x (rise over run).