2.3 Linear, Quadratic or Exponential

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 a quadratic function?

Back

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

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 a positive real number, and x is the exponent.

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.

Front

What does it mean for a function to have a local maximum?

Back

A local maximum is a point where the function value is higher than all nearby points, indicating a peak in the graph.

Front

What does it mean for a function to have a local minimum?

Back

A local minimum is a point where the function value is lower than all nearby points, indicating a trough in the graph.

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 is the difference between linear growth and exponential growth?

Back

Linear growth increases by a constant amount, while exponential growth increases by a constant percentage.

Front

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

Back

The slope (m) is calculated as m = (y2 - y1) / (x2 - x1) between any two points (x1, y1) and (x2, y2).

Front

What is the y-intercept of a linear function?

Back

The y-intercept is the point where the graph of the function crosses the y-axis, represented by the value of b in the equation y = mx + b.