Identify Linear, Quadratic, and Exponential Functions

Front

What is a linear function?

Back

A linear function is a function that graphs to a straight line. It has a constant rate of change and 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, which can be expressed in the form y = ax^2 + bx + c. Its graph is a parabola that opens upwards or downwards.

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, and x is the exponent. Its graph shows rapid growth or decay.

Front

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

Back

A linear function will have the same first difference between consecutive y-values.

Front

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

Back

A quadratic function will have the same second difference between consecutive y-values.

Front

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

Back

An exponential function will have the same ratio when dividing consecutive y-values.

Front

What is the shape of a linear function's graph?

Back

The graph of a linear function is a straight line that can be increasing, decreasing, or horizontal.

Front

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

Back

The graph of a quadratic function is a parabola, which can open upwards or downwards and has a minimum or maximum point.

Front

What does it mean for a function to have linear growth?

Back

Linear growth means that the function increases by a constant amount over equal intervals.

Front

What does it mean for a function to have exponential growth?

Back

Exponential growth means that the function increases by a constant percentage over equal intervals, leading to rapid increases.