Comparing Linear, Exponential, and Quadratic Functions

Front

What is a linear function?

Back

A linear function is a function that can be graphically represented as a straight line. It has a constant rate of change, which means that for every unit increase in the input (x), the output (y) increases by a fixed amount.

Front

What is the general form of a linear equation?

Back

The general form of a linear equation is y = mx + b, where m is the slope (rate of change) and b is the y-intercept (the value of y when x = 0).

Front

What characterizes an exponential function?

Back

An exponential function is characterized by a constant ratio of change. It can be expressed in the form y = a * b^x, where a is a constant, b is the base (a positive number), and x is the exponent.

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. This means that exponential growth becomes much larger than linear growth over time.

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 does the graph of a quadratic function look like?

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 is the vertex of a parabola?

Back

The vertex of a parabola is the highest or lowest point on the graph, depending on whether it opens upwards or downwards.

Front

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

Back

A linear function will have a constant difference in the y-values for equal increments in the x-values.

Front

What is the common ratio in an exponential function?

Back

The common ratio in an exponential function is the factor by which the output (y) changes for each unit increase in the input (x).

Front

How can you tell if a function is quadratic from its graph?

Back

A function is quadratic if its graph forms a parabola, which is a U-shaped curve.