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3 years ago

The function f(x) = (x − 4)(x − 2) is shown.What is the range of the function?

Mathematics

1 answer:

yuradex [85]3 years ago

3 0

Answer:

The range is y ≥ -1

Step-by-step explanation:

∵ f(x) = (x - 4)(x - 2)

∴ f(x) = x² - 2x - 4x + 8

∴ f(x) = x² - 6x + 8 ⇒ quadratic function (ax² + bx + c) represented by

parabola graphically

∵ a = 1 , b = -6 , c = 8

∴ x-coordinate of its vertex = -b/2a = -(-6)/2×1 = 3

∴ f(3) = (3)² - 6(3) + 8 = -1

∵ a is positive ⇒ the curve has minimum point and it's open upward

∴ the minimum point is (3 , -1)

∴ The range is y ≥ -1 ⇒ because the minimum value is -1

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3 years ago

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