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 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. 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 y = ax^2 + bx + c, where a, b, and c are constants.

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 ratio of change between consecutive y-values when divided by the previous y-value.

Front

What is the general shape of a quadratic function's graph?

Back

The graph of a quadratic function is a parabola, which can open upwards or downwards depending on the sign of the coefficient a.

Front

What type of function best models the height of a ball thrown into the air?

Back

A quadratic function best models the height of a ball thrown into the air, as it follows a parabolic trajectory.

Front

What type of function best models a constant hourly wage?

Back

A linear function best models a constant hourly wage, as the total earnings increase at a constant rate.

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, represented by the value of b in the equation y = mx + b.

Front

What does the slope represent in a linear function?

Back

The slope (m) represents the rate of change of the function, indicating how much y changes for a unit change in x.