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To graph the equation, choose three values for x and list them in a table. (Hint: choose values that are easy to calculate, like ?1, 0, and 1.) Substitute each value in the equation and simplify to find the corresponding y-coordinate. Plot the ordered pairs and draw a straight line through the points.

The picture of the tile figures may also be described by an equation in y = mx + b form, where x and y are variables and m represents the growth rate and b represents the starting value of the pattern.

How To: Given a graph, use the vertical line test to determine if the graph represents a function. Inspect the graph to see if any vertical line drawn would intersect the curve more than once. If there is any such line, the graph does not represent a function.

Chaos theory is the study of deterministic difference (differential) equations that display sensitive dependence upon initial conditions (SDIC) in such a way as to generate time paths that look random.

Chaos Theory This equation is May's logistic map. It describes a process evolving through time ? xt+1, the level of some quantity x in the next time period ? is given by the formula on the right, and it depends on xt, the level of x right now. k is a chosen constant.

Writing an Equation for a Line of Best Fit on a Scatterplot - YouTube YouTube Start of suggested clip End of suggested clip Times X plus whatever our y-intercept is okay by looking at this graph it appears that our y-MoreTimes X plus whatever our y-intercept is okay by looking at this graph it appears that our y-intercept. Right up here is a little bit more than 120. So maybe we can put like 121.

Bifurcation diagram of the logistic map x ? r x (1 ? x). Each vertical slice shows the attractor for a specific value of r. The diagram displays period-doubling as r increases, eventually producing chaos.