Comparing Linear, Quadratic, Exponential [Moderate]

Front

What is a linear function?

Back

A linear function is a function that can be graphically represented in the Cartesian plane 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 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, where a, b, and c are constants and a ≠ 0.

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.

Front

How does a linear function increase?

Back

A linear function increases at a constant rate, represented by the slope (m) in the equation y = mx + b.

Front

How does a quadratic function behave as x increases?

Back

A quadratic function can either open upwards or downwards, and its rate of increase or decrease accelerates as x moves away from the vertex.

Front

What is the growth rate of an exponential function?

Back

An exponential function grows at a rate proportional to its current value, leading to rapid increases as x becomes larger.

Front

What is the difference between linear and exponential growth?

Back

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

Front

What type of relationship does Payment Plan 1 represent?

Back

Payment Plan 1 represents a linear relationship, as the amount increases by a fixed amount ($5) each week.

Front

What type of relationship does Payment Plan 2 represent?

Back

Payment Plan 2 represents an exponential relationship, as the amount increases by a percentage (5%) each week.

Front

What is the general form of a quadratic equation?

Back

The general form of a quadratic equation is y = ax^2 + bx + c.