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f(x)=-3x+1quad[-2,2

f(x)=−3x+1[−2,2f(x)=-3x+1\quad[-2,2

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Full solution

Q. f(x)=−3x+1[−2,2f(x)=-3x+1\quad[-2,2
  1. Calculate f(−2)f(-2): Calculate f(−2)f(-2) and f(2)f(2) to find the function values at the endpoints of the interval.\newlinef(−2)=−3(−2)+1=6+1=7f(-2) = -3(-2) + 1 = 6 + 1 = 7\newlinef(2)=−3(2)+1=−6+1=−5f(2) = -3(2) + 1 = -6 + 1 = -5
  2. Determine function behavior: Determine the behavior of the function over the interval. Since the function is linear and decreasing (coefficient of xx is −3-3), the maximum value occurs at the left endpoint x=−2x = -2 and the minimum value occurs at the right endpoint x=2x = 2.\newlineMaximum value at x=−2x = -2 is 77.\newlineMinimum value at x=2x = 2 is −5-5.
  3. Conclude function range: Conclude the range of the function on the interval [−2,2][-2, 2] is from the minimum value to the maximum value.\newlineRange: [−5,7][-5, 7]

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