Linear, Exponential or Quadratic

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 f(x) = 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. It shows rapid growth or decay.

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. Its graph is a parabola.

Front

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

Back

A linear function will have a constant rate of change between the x-values and y-values. The differences in y-values divided by the differences 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 multiplicative rate of change. The ratio of consecutive y-values will remain constant.

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 does the slope of a linear function represent?

Back

The slope of a linear function 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 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 f(x) = mx + b.

Front

What is the vertex of a quadratic function?

Back

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

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 much faster growth over time.