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) = ( (1)/(2) x) {}^(2)`

`d. \: \: g(x) = (x + 2) {}^(2)`
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Answer 1

9514 1404 393

Answer:

b. g(x) = 2x²

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