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Mathematics

Grade10

Easy

Question

Compare the graph of $h open parentheses x close parentheses equals 4 to the power of x minus 3 end exponent plus 5$ to the graph of $h open parentheses x close parentheses equals 4 to the power of x end exponent$ .

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

hint Hint:

we know that $g open parentheses x close parentheses equals a to the power of x minus h end exponent$ is the horizontal translation of $f open parentheses x close parentheses equals a to the power of x end exponent$ by $h$ units. If h is greater than 0 the graph will move right and if h is less than 0 the graph will move left. f(x)= $a to the power of x$ +k is the vertical translation of the graph f(x)= $a to the power of x$ , where the graph moves upward by k units.

The correct answer is: 3 units to the right and 5 units up

The graph of $f left parenthesis x right parenthesis equals a to the power of x minus h end exponent$ is a horizontal translation of the graph of $f left parenthesis x right parenthesis equals a to the power of x end exponent$ . If h is greater than 0 the graph will move right.
The graph of $f left parenthesis x right parenthesis equals a to the power of x end exponent plus k$ is a vertical translation of the graph of $f left parenthesis x right parenthesis equals a to the power of x end exponent$ . The graph will move upward.
In $h open parentheses x close parentheses equals 4 to the power of x minus 3 end exponent plus 5$ , the graph of the parent function is translated both horizontally and vertically.
It is translated 3 units to the right and 5 units up.

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