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P.1 Graphs and Models

P.1 Graphs and Models. I’m so. to be in Calculus!!!. Sketching a Graph by Point Plotting. Sketch the graph of y = x 2 - 2. x y. -2 -1 0 1 2 3. 2 -1 -2 -1 2 7. Finding x- and y-intercepts. Find the x- and y-intercepts of the graph of y = x 3 - 4x.

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P.1 Graphs and Models

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  1. P.1 Graphs and Models I’m so to be in Calculus!!!

  2. Sketching a Graph by Point Plotting Sketch the graph of y = x2 - 2 x y -2 -1 0 1 2 3 2 -1 -2 -1 2 7

  3. Finding x- and y-intercepts

  4. Find the x- and y-intercepts of the graph of y = x3 - 4x To find the x-intercepts, let y be zero and solve for x. 0 = x3 - 4x This factors into? x(x - 2)(x + 2) = 0 the graph has the three x-intercepts: (0,0), (2,0), (-2,0) x = 0, 2, or -2 To find the y-intercepts, let x = 0. y = 03 - 4(0) This produces y = 0. So, the y-intercept is (0,0).

  5. Symmetry (x,y) (-x,y) (x,y) (x,y) (x,-y) (-x,-y) x-axis origin y-axis (-x,y) , (x,-y) , and (-x,-y) are the key points in determining symmetry.

  6. Check for symmetry with respect to both axes and the origin. Ex. 4 xy3 + 10 = 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) Is this, or can we get this to look like the original? (-x)y3 + 10 = 0 -xy3 + 10 = 0 No. x-axis (x,-y) x(-y)3 + 10 = 0 -xy3 + 10 = 0 Not like the original. origin (-x,-y) (-x)(-y)3 + 10 = 0 This graph has origin symmetry. xy3 + 10 = 0

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