Presentation on theme: "P.1 Graphs and Models I’m so to be in Calculus!!!."— Presentation transcript:
P.1 Graphs and Models I’m so to be in Calculus!!!
Sketching a Graph by Point Plotting Sketch the graph of y = x x y
Finding x- and y-intercepts
Find the x- and y-intercepts of the graph of y = x 3 - 4x To find the x-intercepts, let y be zero and solve for x. 0 = x 3 - 4x This factors into? x(x - 2)(x + 2) = 0 x = 0, 2, or -2 the graph has the three x-intercepts: (0,0), (2,0), (-2,0) To find the y-intercepts, let x = 0. y = (0) This produces y = 0. So, the y-intercept is (0,0).
Symmetry y-axis x-axisorigin (x,y)(-x,y)(x,y) (x,-y) (x,y) (-x,-y) (-x,y), (x,-y), and (-x,-y) are the key points in determining symmetry.
Check for symmetry with respect to both axes and the origin. Ex. 4 xy = 0 Plug in the three ordered pairs. If you can get it to look like the original equation, it has that symmetry. y-axis (-x,y) (-x)y = 0 -xy = 0 Is this, or can we get this to look like the original? No. x-axis (x,-y)x(-y) = 0 -xy = 0Not like the original. origin (-x,-y) (-x)(-y) = 0 xy = 0 This graph has origin symmetry.