Functions Types: Graphs

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 a radical function?

Back

A radical function is a function that contains a variable within a radical (square root, cube root, etc.), typically in the form f(x) = √(x) or f(x) = x^(1/n).

Front

What is a rational function?

Back

A rational function is a function that can be expressed as the ratio of two polynomials, typically in the form f(x) = P(x)/Q(x), where P and Q are polynomials and Q(x) ≠ 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 function that returns the non-negative value of its input, typically in the form f(x) = |x|.

Front

What is the general shape of a quadratic function's graph?

Back

The graph of a quadratic function is a parabola, which opens upwards if the leading coefficient (a) is positive and downwards if it is negative.

Front

How can you identify a radical function from its graph?

Back

A radical function's graph typically has a curved shape that starts at a point (the vertex) and extends to the right, often resembling half of a sideways parabola.

Front

What are the key characteristics of a rational function's graph?

Back

A rational function's graph may have vertical asymptotes (where the function is undefined) and horizontal asymptotes, and it can exhibit breaks or holes.

Front

What distinguishes an exponential function from a linear function?

Back

An exponential function grows or decays at a rate proportional to its current value, while a linear function grows at a constant rate.

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 the parabola opens.