Linear, Exponential and Quadratic Functions ET

Front

What is the general form of a linear function?

Back

A linear function can be expressed in the form f(x) = mx + b, where m is the slope and b is the y-intercept.

Front

What is the general form of an exponential function?

Back

An exponential function can be expressed in the form f(x) = a * b^x, where a is a constant, b is the base, and x is the exponent.

Front

What is the general form of a quadratic function?

Back

A quadratic function 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 identify a quadratic function from its equation?

Back

A quadratic function can be identified by the presence of the x^2 term, which indicates that the function is parabolic.

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.

Front

What are the characteristics of a quadratic function's graph?

Back

The graph of a quadratic function is a parabola that opens upwards or downwards, depending on the sign of the leading coefficient (a).

Front

What does it mean for a function to be exponential?

Back

A function is exponential if it grows or decays at a rate proportional to its current value.

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 the direction the parabola opens.

Front

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

Back

You can determine the type of function by analyzing the differences (for linear) or ratios (for exponential) between consecutive values.

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(x) when x = 0.