Linear, Exponential and Quadratic Functions ET

Front

What is a linear function?

Back

A linear function is a function that graphs to a straight line. It can be expressed in 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 f(x) = a * b^x, where a is a constant, b is the base (b > 0), and x is the exponent. It shows rapid growth or decay.

Front

What is a quadratic function?

Back

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

Front

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

Back

A linear function will have a constant rate of change, meaning the difference between consecutive y-values divided by the difference in x-values will be the same.

Front

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

Back

An exponential function will show a constant multiplicative rate of change, meaning the ratio of consecutive y-values will be constant.

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 a > 0 and downwards if a < 0.

Front

What does the vertex of a quadratic function represent?

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 significance of the y-intercept in a linear function?

Back

The y-intercept is the point where the graph of the function crosses the y-axis, representing the value of y when x = 0.

Front

What is the significance of the slope in a linear function?

Back

The slope indicates the steepness of the line and the direction of the relationship between x and y; a positive slope means y increases as x increases.

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.