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Jonathan Houston
Mathematics
21 October, 19:55
How is g (x) = x^2-11 related to f (x) = x^2
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Rose Davis
21 October, 20:14
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G (x) x^2-11 is a translation of f (x) x^2 shifted 11 units down
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Wilson Ball
21 October, 20:17
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Translation 11 units down
Step-by-step explanation:
Our parent function is f (x) = x². Our new function is g (x) = x² - 11.
This is a type of transformation - a translation specifically. We need to figure out if this is a vertical or a horizontal translation. Vertical transformations alter the entire function while horizontal transformations alter only the x. We see that in g (x), the - 11 is on the entire function (if it was g (x) = (x - 11) ², then it'd be horizontal).
So, since we have "-" 11 and not "+" 11, we know that this is a vertical translation 11 units down.
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