What is the range of the function $2 {(x - 3)}^{2} + 1$ $2(x-3)^2+1$ ?

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What is the range of the function $2 {(x - 3)}^{2} + 1$ $2(x-3)^2+1$ ?

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Answer 1 · 2018-01-12T13:21:09

Range: $f (x) \in [1, + \infty)$ $f(x) in [1,+oo)$

Explanation:

Note that ${(x - 3)}^{2}$ $(x-3)^2$ has a minimum value of $0$ $color(blue)0$
in which case $2 {(x - 3)}^{2} + 1$ $2(x-3)^2+1$ has a value of $1$ $color(red)1$

Also note that ${(x - 3)}^{2}$ $(x-3)^2$ has no upper limit
so as the value of ${(x - 3)}^{2}$ $(x-3)^2$ increases $2 {(x - 3)}^{2} + 1 \to + \infty$ $2(x-3)^2+1 rarr +oo$

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What is the range of the function $2 {(x - 3)}^{2} + 1$ $2(x-3)^2+1$ ?

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