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If the function f is defined by the equation f(x) = k(x + 6)(x − 1), where k > 5, t hen which of t he following is equivalent to f(7) ?
- a)f(−78)
- b)f(−12)
- c)f(−2)
- d)f(78)
Correct answer is option 'B'. Can you explain this answer?
Most Upvoted Answer
If the function f is defined by the equation f(x) = k(x + 6)(x −...
One way to tackle this question is simply to simplify the expression for f(7), and then see which choice gives the same expression.
f(7) = k(7 + 6)(7 - 1) = k(13)(6) = 78k
Evaluate (A): f(-78) = k(-78 + 6)(-78 - 1) = k(-72)(-79) = 5,688k
Evaluate (B): f(-12) = k(-12 + 6)(-12 - 1) = k(-6)(-13) = 78k
Evaluate (C): f(-2) = k(-2 + 6)(-2 - 1) = k(4)(-3) = -12k
Evaluate (D): f(78) = k(78 + 6)(78 - 1) = k(84)(77) = 6,468k
This shows that f(-12) is equal to f(7). Alternately, you might just make a quick sketch of the parabola and take advantage of the symmetry:
f(7) = k(7 + 6)(7 - 1) = k(13)(6) = 78k
Evaluate (A): f(-78) = k(-78 + 6)(-78 - 1) = k(-72)(-79) = 5,688k
Evaluate (B): f(-12) = k(-12 + 6)(-12 - 1) = k(-6)(-13) = 78k
Evaluate (C): f(-2) = k(-2 + 6)(-2 - 1) = k(4)(-3) = -12k
Evaluate (D): f(78) = k(78 + 6)(78 - 1) = k(84)(77) = 6,468k
This shows that f(-12) is equal to f(7). Alternately, you might just make a quick sketch of the parabola and take advantage of the symmetry:
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If the function f is defined by the equation f(x) = k(x + 6)(x − 1), where k > 5, t hen which of t he following is equivalent to f(7) ?a)f(−78)b)f(−12)c)f(−2)d)f(78)Correct answer is option 'B'. Can you explain this answer?
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