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maksim [4K]
3 years ago
15

What is the range of the function f(x) = 3x2 + 6x – 8?

Mathematics
1 answer:
Fudgin [204]3 years ago
3 0

Answer:

Range → {y| y ≥ -11}

Step-by-step explanation:

Range of a function is the set of of y-values.

Given function is,

f(x) = 2x² + 6x - 8

By converting this equation into vertex form,

f(x) = 3(x^2+2x-\frac{8}{3})

     = 3(x^2+2x+1-1-\frac{8}{3})

     = 3[(x+1)^2-\frac{11}{3}]

     = 3(x+1)^2-11

Vertex of the parabola → (-1, -11)

Therefore, range of the function will be → y ≥ -11

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We can see the pattern

a_5=a_8=a_{11}=a_{14}=...=5\\ \\a_6=a_9=a_{12}=a_{15}=...=8\\ \\a_7=a_{10}=a_{13}=a_{16}=...=11

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a_{3k-1}=5\\ \\a_{3k}=8\\ \\a_{3k+1}=11

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