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 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 mathematical function of the form f(x) = a * b^x, where a is a constant, b is the base (a positive real number), and x is the exponent.

Front

What is a quadratic function?

Back

A quadratic function is a polynomial function of degree 2, typically in the form f(x) = ax^2 + bx + c, where a, b, and c are constants and a ≠ 0.

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 in y-values divided by the difference in x-values will be the same for all intervals.

Front

What does the slope (m) represent in the equation y = mx + b?

Back

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

Front

What is the y-intercept in the equation y = mx + b?

Back

The y-intercept (b) is the value of y when x = 0; it is the point where the line crosses the y-axis.

Front

What is the general shape of a quadratic function when graphed?

Back

A quadratic function graphs as a parabola, which can open upwards or downwards depending on the sign of the coefficient a.

Front

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

Back

A quadratic function will show a constant second difference in the y-values when the x-values are evenly spaced.

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, leading to faster growth over time.

Front

What is the standard form of a quadratic function?

Back

The standard form of a quadratic function is f(x) = a(x - h)^2 + k, where (h, k) is the vertex of the parabola.