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Mathematics

Grade10

Easy

Question

The exponential function $g open parentheses x close parentheses equals 4 to the power of x plus 3 end exponent$ is _ units to the _ of the parent function $f open parentheses x close parentheses equals 4 to the power of x end exponent$ .

3 units, right
1 unit, left
1 units, right
3 unit, 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.

The correct answer is: 3 unit, left

$g open parentheses x close parentheses equals a to the power of x minus h end exponent$ is the translation of $f open parentheses x close parentheses equals a to the power of x end exponent$ by $h$ units.
If h > 0, the graph is translated to the right by $h$ units.
If h < 0, the graph is translated to the left by $h$ units.
The graph of $g open parentheses x close parentheses equals 4 to the power of x plus 3 end exponent$ is 3 units to the left of $f open parentheses x close parentheses equals 4 to the power of x end exponent$ .

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