Friday, October 30, 2020

Using intercepts and symmetry to sketch a graph

By Nhat Nguyen at 7:55 AM    No comments
Problem Solution
y = 2 - 3x

y = 2-3(0) = 22, y-intercept
y = 2 - 3(x) -> 3x
2 -> x = (2/3), x-intercept
Symmetry: None

y = 2 - 3x graph
y = (2/3)x + 1

y = (2/3)(0) + 1 = 1, y-intercept

0 = (2/3) x + 1 -> - (2/3)x ->

x = -(3/2), x-intercept

Symmetry: None

y (2/3) x + 1 graph
y = 9 - x^2

y = 9 - (0)^2 = 9, y-intercept
0 = 9 -x^2 -> x^2 =

9 -> x = -+, x-intercepts

intercepts: (0, 9), (3, 0), (-3,0)

y = 9 - (-x)^2 = 9 - x^2

y = 9 - (-x)^2 = 9 - x^2

y = 9 - x^2 graph
y = 2x^2 + x

y = 2x^2 + x = x(x+1)


0 = x(2x + 1) -> x =

0, -(1/2), x-intercepts

symmetry none

y = 2x^2 + x
y = x^3 + 2

y = 0^3 + 2 = 2, y-intercept

0 = x^3 + 2 -> x^3

-2 -> x = \sqrt[3][2,] x-intercept

intercepts: (-\sqrt[3][2,0]), (0,2)

y = x^3 + 2 graph
y = x^3 - 4x

y = 0^3 - 4(0) = 0, y-intercept

x^3 - 4x = 0

x(x^2 - 4) = 0
y = x sqrt(x + 5)







y = sqrt(25 - x^2)











x = y^3






x = y^2 - 4









y (8/x)



y = (10/x^2+1)




y = 6 - |x|


y = |6 - x|



y^2 - x = 9




x^2 + 4y^2 = 4






x + 3y^2 = 6





3x - 4y^2 = 8





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