Given: F(x) = 2x 2 + 1, G(x) = 2x - 1, H(x) = x G -1 (x) =
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Answer:
Step-by-step explanation:
The hyperbola has x-intercepts, so it has a horizontal transverse axis.
The standard form of the equation of a hyperbola with a horizontal transverse axis is
The center is at (h,k).
The distance between the vertices is 2a.
The equations of the asymptotes are
1. Calculate h and k. The hyperbola is symmetric about the origin, so
h = 0 and k = 0
2. For 'a': 2a = x₂ - x₁ = 3 - (-3) = 3 + 3 = 6
a = 6/2 = 3
3. For 'b': The equation for the asymptote with the positive slope is
Thus, asymptote has the slope of
4. The equation of the hyperbola is
The attachment below represents your hyperbola with x-intercepts at ±3 and asymptotes with slope ±2.
