Compare Linear, Quadratic, & Exponential 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 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

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

Back

A linear function will have a constant difference between consecutive y-values for equal intervals of x.

Front

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

Back

A quadratic function will have a constant second difference between 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 have a constant ratio between consecutive y-values for equal intervals of x.

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 vertex of a quadratic function?

Back

The vertex is the highest or lowest point of the parabola, depending on the direction it opens.

Front

What does the term 'common difference' refer to?

Back

The common difference is the constant amount that is added to each term in an arithmetic sequence.

Front

What does the term 'common ratio' refer to?

Back

The common ratio is the constant factor by which each term in a geometric sequence is multiplied to get the next term.