Linear, Exponential, and Quadratic 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 y = mx + b, where m is the slope and b is the y-intercept.

Front

What is an exponential function?

Back

An exponential function is a mathematical function of the form y = ab^x, where a is a constant, b is the base (a positive real number), and x is the exponent. The graph of an exponential function increases or decreases rapidly.

Front

What is a quadratic function?

Back

A quadratic function is a polynomial function of degree 2, typically written in the form y = ax^2 + bx + c, where a, b, and c are constants. Its graph is a parabola.

Front

What is the y-intercept of a function?

Back

The y-intercept of a function is the point where the graph of the function crosses the y-axis. It is found by setting x = 0 in the function's equation.

Front

How do you identify a linear function from a table of values?

Back

A linear function will have a constant rate of change between the x-values and y-values. This means that the difference in y-values divided by the difference in x-values will be the same for all pairs of points.

Front

How do you identify an exponential function from a table of values?

Back

An exponential function will show a constant multiplicative rate of change. This means that the ratio of consecutive y-values will be constant when the x-values increase by the same amount.

Front

What is the general form of a quadratic function?

Back

The general form of a quadratic function is y = ax^2 + bx + c, where a, b, and c are constants and a ≠ 0.

Front

What does the vertex of a parabola represent in a quadratic function?

Back

The vertex of a parabola is the highest or lowest point on the graph of a quadratic function, depending on whether it opens upwards or downwards.

Front

What is the difference between linear and quadratic functions?

Back

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

Front

What is the formula for finding the slope of a linear function?

Back

The slope (m) of a linear function can be calculated using the formula m = (y2 - y1) / (x2 - x1) for any two points (x1, y1) and (x2, y2) on the line.