Fall 2024: Unit 13 Test Comparing Functions

A linear function is a function that graphs to a straight line. It can be expressed in the form y = mx + b, where m is the slope and b is the y-intercept.

Linear growth increases by a constant amount over equal intervals, while exponential growth increases by a constant percentage over equal intervals.

The slope represents the rate of change of the function; it indicates how much y changes for a unit change in x.

The y-intercept is the value of y when x is 0; it is the point where the line crosses the y-axis.

A linear graph will form a straight line when plotted on a coordinate plane.

The initial fee is a fixed cost that must be paid before any additional costs, such as monthly fees, are incurred.

A shift left means that the graph of the function moves horizontally to the left on the coordinate plane, typically represented by a change in the x-value.

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

The general form of an exponential growth function is y = a(1 + r)^t, where a is the initial amount, r is the growth rate, and t is time.

A quadratic function is a polynomial function of degree 2, typically expressed in the form y = ax^2 + bx + c.