Linear, Exponential and Quadratic Functions ET

Front

What type of function best models a situation where you earn a fixed hourly wage?

Back

Linear function.

Front

What is the defining characteristic of an exponential function?

Back

An exponential function has a constant ratio of change, meaning it grows or decays by a constant percentage over equal intervals.

Front

How can you identify an exponential function from a set of data points?

Back

If the ratio of consecutive values is constant, the function is likely exponential.

Front

What is the general form of an exponential function?

Back

The general form is f(x) = a * b^x, where 'a' is a constant and 'b' is the base of the exponential.

Front

What type of function is represented by a quadratic equation?

Back

A quadratic function is represented by a polynomial of degree 2, typically in the form f(x) = ax^2 + bx + c.

Front

What is the shape of the graph of a quadratic function?

Back

The graph of a quadratic function is a parabola.

Front

What distinguishes a linear function from a quadratic function?

Back

A linear function has a constant rate of change (a straight line), while a quadratic function has a variable rate of change (a curve).

Front

What is the standard form of a linear function?

Back

The standard form is f(x) = mx + b, where 'm' is the slope and 'b' is the y-intercept.

Front

What does it mean for a function to be quadratic?

Back

A function is quadratic if it can be expressed in the form f(x) = ax^2 + bx + c, where a, b, and c are constants and a ≠ 0.

Front

How can you determine if a function is linear, quadratic, or exponential from a table of values?

Back

Check the differences between consecutive values (linear), the ratios of consecutive values (exponential), or the second differences (quadratic).