Topic 3: Linear Functions (enVision Algebra 1)

A recursive formula defines each term of a sequence using the previous term(s). For example, for the sequence -5, -8.5, -12, -15.5, -19, the recursive formula is $$a_n = a_{n-1} - 3.5; a_1 = -5$$ .

The graph of g is a vertical translation down by 5 units compared to the graph of f. This is indicated by the constant term -5.

A negative association indicates that as one variable increases, the other variable tends to decrease.

No association indicates that there is no discernible relationship between the two variables being plotted.

The domain is the set of all first elements (x-values) from the ordered pairs.

The range is the set of all second elements (y-values) from the ordered pairs.

The formula is $$a_n = a_1 + (n-1)d$$ , where $$a_1$$ is the first term and $$d$$ is the common difference.

The common difference is the amount added (or subtracted) to each term to get to the next term in the sequence.

A linear function is a function that can be graphically represented as a straight line, typically in the form $$f(x) = mx + b$$ , where $$m$$ is the slope and $$b$$ is the y-intercept.

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