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Alex Ar [27]
3 years ago
7

Determine the domain of the function f(x)=1/3x^2+10x+8

Mathematics
1 answer:
cricket20 [7]3 years ago
8 0
The function is
f(x) = (1/3)x² + 10x + 8

Write the function in standard form for a parabola.
f(x) = (1/3)[x² + 30x] + 8
      = (1/3)[ (x+15)²- 225] + 8
      = (1/3)(x+15)² -75 + 8
f(x) = (1/3)(x+15)² - 67

This is a parabola with vertex at (-15, -67).
The axis of symmetry is x = -15
The curve opens upward because the coefficient of x² is positive.
As x -> - ∞, f -> +∞.
As x -> +∞, f -> +∞
The domain is all real values of x (see the graph below).

Answer: The domain is (-∞, ∞)

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