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Mathematics

Grade10

Easy

Question

The graph of g is a translation of 5 units to the left of the graph of $f open parentheses x close parentheses equals 7 to the power of x end exponent$ . What is g?

$g (x) = 5^{x - 7}$
$g (x) = 7^{x} - 5$
$g (x) = 5^{x} - 7$
$g (x) = 7^{x + 5}$

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. So, if the graph is moving 5 units to the left that means h is less than 0 i.e., -5.

The correct answer is: $g open parentheses x close parentheses equals 7 to the power of x plus 5 end exponent$

The graph of $g left parenthesis x right parenthesis$ is translated horizontally to the left.
The graph of $f left parenthesis x right parenthesis equals 2 to the power of x minus h end exponent$ is a horizontal translation of the graph of $f left parenthesis x right parenthesis equals 2 to the power of x end exponent$
If $h$ is positive, the graph is translated to the right.
If $h$ is negative, the graph is translated to the left.
So, the equation of g changes as $g open parentheses x close parentheses equals 7 to the power of x plus 5 end exponent$

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