Question

The functions f(x) and g(x) are shown on the graph. f(x)=x² what is g(x)?

$a. \: \: g(x) = ( x - 2) {}^{2}$
$b. \: \: g(x) = 2 {x}^{2}$
$c. \: \: g(x) = ( \frac{1}{2} x) {}^{2}$
$d. \: \: g(x) = (x + 2) {}^{2}$
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Answer 1

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Answer:

  b.  g(x) = 2x²

Step-by-step explanation:

The vertices of the two curves are in the same place, so no translation has taken place. This eliminates choices 'a' and 'd'.

A point on the curve g(x) is given. You can test to see which of choices 'b' and 'c' it satisfies.

  B: g(2) = 2(2²) = 8 . . . . matches point (2, 8)

  C: g(2) = (1/2·2)² = 1² = 1 . . . . does not match point (2, 8)

The function g(x) is ...

  g(x) = 2x²