Linear, Exponential and Quadratic Functions ET

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 = a * b^x, where a is a constant, b is the base (a positive real number), and x is the exponent. It grows rapidly as x increases.

Front

What is a quadratic function?

Back

A quadratic function is a polynomial function of degree 2, typically in the form y = ax^2 + bx + c, where a, b, and c are constants and a ≠ 0. Its graph is a parabola.

Front

How can 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. The differences in y-values divided by the differences in x-values will be the same.

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 does the slope of a linear function represent?

Back

The slope of a linear function represents the rate of change of y with respect to x. It indicates how much y changes for a unit change in x.

Front

What is the y-intercept in a linear function?

Back

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

Front

How do you determine if a function is quadratic from its graph?

Back

A quadratic function's graph is a parabola, which can open upwards or downwards. It has a vertex, and it is symmetric about a vertical line called the axis of symmetry.

Front

What is the difference between linear and exponential growth?

Back

Linear growth increases by a constant amount, while exponential growth increases by a constant percentage, leading to much faster growth over time.

Front

What is the standard form of a quadratic function?

Back

The standard form of a quadratic function is y = a(x - h)^2 + k, where (h, k) is the vertex of the parabola.