What is the range of $- 2 x^{2} + 4 x - 7$

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Solution

Assuming that the domain of the given function is the set of all real numbers R, so that the variable x takes all values in the interval
$(- \infty, + \infty)$
If x takes all values in the interval $(- \infty, + \infty)$ then 4 x + 5 takes all values in the interval $(- \infty, + \infty)$ and the range of the given function is given by the interval $(- \infty, + \infty)$

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Which of these statements hold true?

i.) $4 (x - 5) = 4 x - 5$

ii.) $x (3 x + 2) = 3 x^{2} + 2$

iii.) $2 x^{2} + 4 (2 x) + 7 = 2 x^{2} + 8 x + 7$ [4 MARKS]

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