Classifying Functions

Front

What is a linear function?

Back

A linear function is a function that can be graphically represented as a straight line. It has the form f(x) = mx + b, where m is the slope and b is the y-intercept.

Front

What is a quadratic function?

Back

A quadratic function is a polynomial function of degree 2, typically in the form f(x) = ax² + bx + c, where a, b, and c are constants and a ≠ 0.

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 (a positive real number), and x is the exponent.

Front

What is a radical function?

Back

A radical function is a function that contains a variable within a radical (square root, cube root, etc.). The general form is f(x) = √(x) or f(x) = n√(x), where n is a positive integer.

Front

What is an absolute value function?

Back

An absolute value function is a function that returns the non-negative value of a number. It is defined as f(x) = |x|, which means the distance of x from 0 on the number line.

Front

How do you identify a linear function from a graph?

Back

A linear function will show a straight line when graphed. It has a constant rate of change, meaning the slope is the same between any two points.

Front

How do you identify a quadratic function from a graph?

Back

A quadratic function will graph as a parabola, which can open upwards or downwards. It has a vertex and may have one or two x-intercepts.

Front

How do you identify an exponential function from a graph?

Back

An exponential function will show a rapid increase or decrease. The graph will not touch the x-axis and will have a horizontal asymptote.

Front

How do you identify a radical function from a graph?

Back

A radical function will have a curve that starts at a point and increases gradually. The graph will not exist for negative values under the square root.

Front

How do you identify an absolute value function from a graph?

Back

An absolute value function will graph as a V-shape. It has a vertex at the minimum point and is symmetric about the vertical line through the vertex.