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Mathematics

Grade10

Easy

Question

Compare the graph of $h open parentheses x close parentheses equals 2 to the power of x plus 5 end exponent minus 7$ to the graph of $h open parentheses x close parentheses equals 2 to the power of x end exponent$ .

7 units up and 5 units to the right
12 units to the right
5 units to the left and 7 units down
2 units left

hint Hint:

We know that the graph of $f left parenthesis x right parenthesis equals 2 to the power of x plus h end exponent$ is a horizontal translation by h units to the left of the graph of $f left parenthesis x right parenthesis equals 2 to the power of x end exponent$ . The graph of $f left parenthesis x right parenthesis equals 2 to the power of x minus k$ is a vertical translation by k unit downwards of the graph of $f left parenthesis x right parenthesis equals 2 to the power of x end exponent$ In $h open parentheses x close parentheses equals 2 to the power of x plus 5 end exponent minus 7$ , the graph of the parent function is translated both horizontally and vertically.

The correct answer is: 5 units to the left and 7 units down

The graph of $f left parenthesis x right parenthesis equals 2 to the power of x plus h end exponent$ is a horizontal translation by h units to the left of the graph of $f left parenthesis x right parenthesis equals 2 to the power of x end exponent$
The graph of $f left parenthesis x right parenthesis equals 2 to the power of x minus k$ is a vertical translation by k unit downwards of the graph of $f left parenthesis x right parenthesis equals 2 to the power of x end exponent$ .
In $h open parentheses x close parentheses equals 2 to the power of x plus 5 end exponent minus 7$ , the graph of the parent function is translated both horizontally and vertically.
It is translated 5 units to the left and 7 units down.

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