Front

What is the definition of a linear function?

Back

A linear function is a function that can be graphically represented in the Cartesian plane 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 the definition of a quadratic function?

Back

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

Front

What is the definition of 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 a positive real number, and x is the exponent.

Front

How do you determine the rate of change from a table of values?

Back

The rate of change can be determined by calculating the difference in the output values (y-values) divided by the difference in the input values (x-values) between two points.

Front

What is a piecewise function?

Back

A piecewise function is a function that is defined by different expressions or formulas for different intervals of the input variable.

Front

What does it mean for a function to be increasing?

Back

A function is increasing on an interval if, for any two points x1 and x2 in that interval, if x1 < x2, then f(x1) < f(x2).

Front

What does it mean for a function to be decreasing?

Back

A function is decreasing on an interval if, for any two points x1 and x2 in that interval, if x1 < x2, then f(x1) > f(x2).

Front

What is the significance of the vertex in a quadratic function?

Back

The vertex of a quadratic function is the highest or lowest point on the graph, depending on the direction of the parabola. It represents the maximum or minimum value of the function.

Front

What is the formula for the vertex of a quadratic function in standard form?

Back

The vertex (h, k) of a quadratic function in standard form f(x) = ax^2 + bx + c can be found using h = -b/(2a) and k = f(h).

Front

What is the difference between a linear and a quadratic relationship?

Back

A linear relationship produces a straight line when graphed, while a quadratic relationship produces a parabolic curve.