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Mathematics

Grade10

Easy

Question

For a given pair $f left parenthesis x right parenthesis equals cube root of 3 x minus 1 end root comma g left parenthesis x right parenthesis equals cube root of 9 x minus 1 end root$ the graph of $g$ is a ___________ of the graph of $f$ .

Vertical stretch
Vertical compression
Horizontal stretch
Horizontal compression

The correct answer is: Horizontal compression

$g left parenthesis x right parenthesis equals cube root of 9 x minus 1 end root equals cube root of 3 left parenthesis 3 x right parenthesis minus 1 end root equals f left parenthesis 3 x right parenthesis comma text where end text k equals 3 greater than 1$
$g left parenthesis x right parenthesis equals f left parenthesis k x right parenthesis text for end text vertical line k vertical line greater than 1$
So, the graph of $g$ is a horizontal compression of graph of $f$ .

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