AA Unit 6: Function Families

Front

What is a function?

Back

A function is a relation that assigns exactly one output for each input. It can be represented as f(x) where x is the input.

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 as f(x) = ax^2 + bx + c, where a, b, and c are constants.

Front

What is an exponential function?

Back

An exponential function is a mathematical function of the form f(x) = a * b^x, where a is a constant, b is the base, and x is the exponent.

Front

What is the absolute value function?

Back

The absolute value function, denoted as |x|, returns the non-negative value of x, meaning it measures the distance of x from zero on the number line.

Front

How can you identify a linear function from a graph?

Back

A linear function will produce a straight line when graphed, indicating a constant rate of change.

Front

What is the general form of a quadratic equation?

Back

The general form of a quadratic equation is ax^2 + bx + c = 0, where a ≠ 0.

Front

What is the vertex of a quadratic function?

Back

The vertex of a quadratic function is the highest or lowest point on the graph, depending on the direction of the parabola.

Front

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

Back

A linear function has a constant slope and produces a straight line, while a quadratic function has a variable slope and produces a parabolic curve.

Front

What does it mean for a function to be non-linear?

Back

A non-linear function does not have a constant rate of change and cannot be represented by a straight line.