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Mathematics

Grade10

Easy

Question

The function $g left parenthesis x right parenthesis equals$ ________ obtained when the graph of $f left parenthesis x right parenthesis equals vertical line x vertical line$ is shifted 3 units right and 1 unit up.

$| x + 3 | + 1$
$| x - 3 | + 1$
$| x + 3 | - 1$
$| x - 3 | - 1$

The correct answer is: $vertical line x minus 3 vertical line plus 1$

For a given $g left parenthesis x right parenthesis equals f left parenthesis x minus h right parenthesis plus k$
the graph of the function $g$ is the graph of function $f$ translated $h$ units horizontally, then translated $k$ units vertically.
$h equals 3 comma k equals 1$
So, the function $g left parenthesis x right parenthesis equals f left parenthesis x minus h right parenthesis plus k equals vertical line x minus 3 vertical line plus 1$

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