Linear, Exponential, Quadratic: Which is it?

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 its graph?

Back

A linear function's graph is a straight line, which means it has a constant rate of change (slope).

Front

What does the term 'slope' refer to in a linear function?

Back

The slope is a measure of the steepness of the line, calculated as the change in y divided by the change in x (rise/run).

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 is the vertex of a parabola?

Back

The vertex is the highest or lowest point of the parabola, depending on its orientation (upward or downward).

Front

What is exponential growth?

Back

Exponential growth occurs when a quantity increases by a consistent percentage over equal time intervals, resulting in a rapid increase.

Front

What is exponential decay?

Back

Exponential decay occurs when a quantity decreases by a consistent percentage over equal time intervals, leading to a rapid decrease.

Front

How do you determine if a function is exponential?

Back

A function is exponential if it can be expressed in the form f(x) = a * b^x, where b > 1 for growth or 0 < b < 1 for decay.