2f(x) = 2x - 4 [0, 3]3f(x) = 3x - 1 [-2, -1]9f(x) = x² [4, 5]4f(x) = 4x [5, 20]5f(x) = x² - 3 [0, 5]1f(x) = x + 10 [-5, -1]10f(x) = 10x [-3, 0]¹/₂f(x) = 0.5x - 2 [2, 4]11f(x) = 2x² + x [1, 4]-1f(x) = -x + 2 [-3, 5]Domainthe set of all reasonable input values of x for the functionRangeset of output y values for the domain of the functionAverage Rate of ChangeChange in values over a given interval.Origin(0,0) on the coordinate graphing system; where the two axes meetx-axisthe horizontal number line in the coordinate systemy-axisthe vertical number line in the coordinate systemCoordinatesany specific (x,y) in the coordinate systemx-interceptwhere the function intersects the x-axisy-interceptwhere the function intersects the y-axis; the b value in a linear functionLinear FunctionA function whose graph is a straight line, where the average rate of change (slope) is constant.Exponential FunctionA function where the average rate of change is not constant and whose input value is an exponent.Table of ValuesA table showing two sets of related numbers<span>Slope of line through the points (-2, 3) and (0,0) m = (0 - 3) / (0 - -2) = -3/2</span><span>Average Rate of Change on the interval [-2, 0]</span>Slope: m = "rise over run" = 2Rate of Change<span>Slope of line through the points (5, -1) and (0,0) m = (0 - -1) / (0 - 5) = -1/5</span><span>Average Rate of Change on the interval [0, 5]</span><span>Slope of line through the points (0, 16) and (4, 21) m = (21 - 16) / (4 - 0) = 5/4</span>Average Rate of Change over the interval [0,4]
Let point be the point where the straight line drawn from point meets the straight line , it is evident that and is similar given that both triangles share the same angle, . Hence, the ratio of the sides of each triangle is the same. Specifically,
