Function Families

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 an absolute value function?

Back

An absolute value function is a piecewise function defined as f(x) = |x|, which outputs the non-negative value of x.

Front

What is the general shape of a linear function graph?

Back

The graph of a linear function is a straight line that can slope upwards or downwards depending on the sign of the slope.

Front

What is the general shape of a quadratic function graph?

Back

The graph of a quadratic function is a parabola, which opens upwards if a > 0 and downwards if a < 0.

Front

What is the general shape of an exponential function graph?

Back

The graph of an exponential function increases rapidly if the base is greater than 1 and approaches zero if the base is between 0 and 1.

Front

What is the general shape of an absolute value function graph?

Back

The graph of an absolute value function forms a V shape, with the vertex at the origin (0,0) if no transformations are applied.

Front

How do you identify a linear function from its equation?

Back

A linear function can be identified by its equation in the form f(x) = mx + b, where the highest exponent of x is 1.

Front

How do you identify a quadratic function from its equation?

Back

A quadratic function can be identified by its equation in the form f(x) = ax² + bx + c, where the highest exponent of x is 2.