Increasing and Decreasing Graphs By: Naiya Kapadia,YiQi Lu, Elizabeth Tran

- Increasing and decreasing lines are determined by the graph's slope, which can be found in the linear equation form, y= mx+b. Linear Function y= -1/4 To tell whether the graph is an increasing function, the slope must be positive, and the graph runs from left to right, as shown in the "increasing graph." To tell whether the graph is a decreasing function,the slope must be negative, and the graph runs from right to left, as shown in the "decreasing graph." Increasing Graph: Decreasing Graph:

- A quadratic function has the form y= ax^2 + bx + c, where "a" cannot equal 0. To tell whether the graph is an increasing function, a > 0 and the graph opens upward. This causes the "x" term of the graph to be positive, as shown in the "increasing graph." To tell whether the graph is a decreasing function, a < 0 and the graph opens downward. This causes the "x" term of the graph to be negative, as shown in the "decreasing graph." Increasing Graph: Decreasing Graph: Quadratic Function

Correlation - Also known as the "best fitting lines", correlation helps show the linear relationship of (a) set(s) of data. To tell whether a correlation graph is increasing, the slope must be positive, gradually progressing from the bottom left to the top right of the grid, such as the example of the "increasing graph." To tell whether a correlation graph is increasing, the slope must be negative, gradually progressing from the top left to the bottom right of the grid, such as the example of the "decreasing graph." Increasing Graph: Decreasing Graph:

Exponential Function Increasing y = ab^x is an exponential growth function when a > 0 and b > 1, which is an increasing function. This is a graph of exponential growth function,the graph has a curving line that is going from the bottom of left up to right, that is an increasing line. To apply the exponential growth function into real life, you can use y = a(1+r)^t for a real life quantity increases by a fixed percent each year. Decreasing y = ab^x is an exponential decay function when a > 0 and 0 < b < 1, which is a decreasing function. With an exponential decay graph, the graph would be a curve line that decreases from the top of left down to the right, which is a curve line of decreasing y = a(1-r)^t can use for a real-life quatity decreases by a fixed percent each year.

Radical Function -y = a√X and y = a 3√X (3√X is a cubic root) are radical functions. - If a > 1, then it would be an increasing function for both y = a√X and y = a 3√X y = a 3√X y = a√X - If a < 1, then it would be a decreasing function for both y = -a√X and y = -a 3√X y = -a 3√X y = -a√X

Logarithmic Function Graph -Logarithmic Functions: y = log b (x - h) + k ~ For a logarithmic function to increase, the "b" value must be greater than 1. The graph is moving up to the right. an increasing graph ~ A decreasing logarithmic function has a "b" value that is 0 < b < 1. The graph moves down to the right. a decreasing graph

Absolute Value - Put into the form of y=a|x-h|+k -The "a" value is almost like the slope. It can be either positive or negative. - If the "a" value is positive, the graph opens upwards as shown in the "increasing graph". -If the "a" value is negative, the graph opens downwards as shown in the "decreasing graph". Increasing graph Decreasing graph

Piecewise Function - A function represented by a combination of equations, each corresponding to a part of the domain. - The equations can be linear, quadratic, polynomial...etc., as long as they have x-value constraints. - The equation of the original graph tells you if the graph is decreasing or increasing or doing both at certain points on the graph. The slope is what determines this aspect of the graph, but the constraint of the domain can change that. Look at example. Example of a piecewise function: Notice that the slope of the first equation is positive, but the graph is going down. This is because the constraint is making the graph look like it's decreasing from that point of -3. The second equation is a negative and stays negative even after the constraint.