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Mathematics

Grade10

Easy

Question

How is the function $f left parenthesis x right parenthesis equals 2 to the power of x$ is translated to obtain the graph of the function $g left parenthesis x right parenthesis equals 2 to the power of x minus 2 end exponent minus 7$

2 units left and 7 units up
2 units right and 7 units down
2 units right and 7 units up
2 units left and 7 units down

The correct answer is: 2 units right and 7 units down

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.
$h equals 2 comma k equals negative 7$
So, to obtain the function $g left parenthesis x right parenthesis$ the graph of the function $f left parenthesis x right parenthesis$ is translated 2 units right and 7 units down.

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