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Mathematics

Grade10

Easy

Question

The parent function of the exponential function $g open parentheses x close parentheses equals 3 to the power of x minus 7 end exponent$ is _______.

$g (x) = 3^{x} + 7$
$g (x) = 3^{x}$
$g (x) = 7^{x}$
$g (x) = 3^{x + 7}$

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 parent function $f open parentheses x close parentheses equals a to the power of x end exponent$ by $h$ units.

The correct answer is: $g open parentheses x close parentheses equals 3 to the power of x end exponent$

$g open parentheses x close parentheses equals a to the power of x minus h end exponent$ is the horizontal translation of $f open parentheses x close parentheses equals a to the power of x end exponent$ by $h$ units.
So, $g open parentheses x close parentheses equals 3 to the power of x minus 7 end exponent$ is the horizontal translation of $g open parentheses x close parentheses equals 3 to the power of x end exponent$ by 7 units to the right.

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