Linear, Quadratic, Exponential, or Cubic?

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 a quadratic function?

Back

A quadratic function is a polynomial function of degree 2, typically in the form f(x) = ax² + 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 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 cubic function?

Back

A cubic function is a polynomial function of degree 3, typically in the form f(x) = ax³ + bx² + cx + d, where a, b, c, and d 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 between consecutive y-values divided by the difference in x-values will be the same.

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 equally spaced.

Front

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

Back

An exponential function will show a constant ratio between consecutive y-values when the x-values are equally spaced.

Front

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

Back

The graph of a quadratic function is a parabola, which opens upwards if a > 0 and downwards if a < 0.

Front

What is the general shape of a cubic function's graph?

Back

The graph of a cubic function can have one or two turning points and can extend to positive or negative infinity in both directions.

Front

What is the significance of the y-intercept in a linear function?

Back

The y-intercept is the point where the graph of the function crosses the y-axis, representing the value of f(0).