P.1 Graphs and Models

I’m so

to be in Calculus!!!

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

Finding x- and y-intercepts

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

x = 0, 2, or -2

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∴ the graph has the three x-intercepts: (0,0), (2,0), (-2,0)

To find the y-intercepts, let x = 0.

y = 03 - 4(0) This produces y = 0. So, the y-intercept is (0,0).

Symmetry

y-axis x-axis origin

(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 andthe 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) (-x)y3 + 10 = 0-xy3 + 10 = 0

Is this, or can weget this to look likethe original? 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

xy3 + 10 = 0

This graph hasorigin symmetry.