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Mathematics

Grade10

Easy

Question

For a given pair $f left parenthesis x right parenthesis equals square root of x minus 1 end root comma g left parenthesis x right parenthesis equals 7 over 9 square root of x minus 1 end root$ the graph of $g$ is a ___________
of the graph of $f$

Vertical stretch
Vertical compression
Horizontal stretch
Horizontal compression

The correct answer is: Vertical compression

$g left parenthesis x right parenthesis equals 7 over 9 square root of x minus 1 end root equals 7 over 9 f left parenthesis x right parenthesis equals 0.77 f left parenthesis x right parenthesis$ where $k equals 0.77 less than 1$
$g left parenthesis x right parenthesis equals k f left parenthesis x right parenthesis text for end text 0 less than vertical line k vertical line less than 1$
So, the graph of $g$ is a vertical compression of the graph of $f$ .

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