Question

The function f(x)=2x2−x+4; f ( x ) = 2 x 2 − x + 4 is defined over the domain 0 ≤ x ≤ 3 Find the range of this function. A. 4 < f(x) < 7 B. 4 < f(x )< 19 C. 4 ≤ f(x) ≤ 19 D. 4 ≤ f(x) ≤ 25

Answer 1

C. 4 ≤ f(x) ≤ 19 . . . . . . best of bad answer choices

Explanation:

When looking for the range of a function on an interval, one must check the function values at the ends of the interval, along with any local maxima or minima.

Here, the function values at the interval ends are ...

f(0) = 4

f(3) = 2·3² -3 +4 = 19

The axis of symmetry is located at ...

x = -b/(2a) = -(-1)/(2(2)) = 1/4

This is a value in the interval, so will be the location of the minimum value of the function.

f(1/4) = 2(1/4)² -1/4 +4 = 3.875

The range of f(x) on the interval [0, 3] is [3.875, 19]:

3.875 ≤ f(x) ≤ 19

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All of the answer choices are incorrect. Please discuss question this with your teacher.