AlgebraVery hardZero of a linear function from two values
Algebra practice question
For the linear function f, f(−2) = 9 and f(4) = −3. For what value of x is f(x) = 0?
Answer: 2.5 or 5/2
Slope = (−3 − 9)/(4 − (−2)) = −2, so f(x) = 9 − 2(x + 2) = 5 − 2x. Then 5 − 2x = 0 gives x = 2.5.
Common wrong answers
- If you answered 1
- 1 is the midpoint of the two x-values, which is the zero only if the two outputs were opposites.
- If you answered 5
- 5 is f(0), the y-intercept, not the zero.
- If you answered -2.5
- −2.5 has the sign wrong.
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