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Mathematics

Grade10

Easy

Question

Identify the function $g left parenthesis x right parenthesis$ obtained when the graph of $f left parenthesis x right parenthesis equals x squared$ is shifted 1 unit left and 2 units up.

$(x - 1)^{2} + 2$
$(x + 1)^{2} - 2$
$(x - 1)^{2} - 2$
$(x + 1)^{2} + 2$

The correct answer is: $left parenthesis x plus 1 right parenthesis squared plus 2$

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 the function $f$ translated $h$ units horizontally, then translated $k$ units vertically.
$h equals negative 1 comma k equals 2$
So, the function $g left parenthesis x right parenthesis equals f left parenthesis x minus h right parenthesis plus k equals left parenthesis x plus 1 right parenthesis squared plus 2$

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