Identify Linear, Quadratic, or Exponential 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 a positive real number, and x is the exponent.

Front

How can you identify a linear function from its graph?

Back

A linear function's graph is a straight line, and it has a constant rate of change (slope).

Front

How can you identify a quadratic function from its graph?

Back

A quadratic function's graph is a parabola, which opens either upwards or downwards, and it has a vertex.

Front

How can you identify an exponential function from its graph?

Back

An exponential function's graph shows rapid growth or decay, and it is not a straight line; it curves upwards or downwards.

Front

What is the general form of a linear equation?

Back

The general form of a linear equation is Ax + By = C, where A, B, and C are constants.

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.

Front

What is the difference between linear and quadratic functions?

Back

Linear functions have a constant rate of change and graph as straight lines, while quadratic functions have a variable rate of change and graph as parabolas.

Front

What is the significance of the base in an exponential function?

Back

The base in an exponential function determines the rate of growth or decay; if the base is greater than 1, the function grows, and if it is between 0 and 1, it decays.