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Mathematics

Grade10

Easy

Question

A company’s logo is modelled by the function $f left parenthesis x right parenthesis equals negative vertical line x vertical line plus 3$ . For a new design, the company wants the logo to be narrower toward the $x minus text axis end text$ . Find the function for the new logo.

$\frac{1}{2} (3 - | x |)$
$2 (3 - | x |)$
$2 (| x | + 3)$
$\frac{1}{2} (| x | + 3)$

The correct answer is: $1 half left parenthesis 3 minus vertical line x vertical line right parenthesis$

To make the logo narrower towards the $x minus text axis end text$ , then the function must be vertically compressed
$g left parenthesis x right parenthesis equals k f left parenthesis x right parenthesis text for end text 0 less than vertical line k vertical line less than 1$
So, the correct function is $1 half left parenthesis 3 minus vertical line x vertical line right parenthesis$ , where $k equals 1 half less than 1$ .

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