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2 answers:
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The parent function for this function is
We have to explain how the given function can be obtained from the parent function.
Let y=g(x)
So,
Notice that x in the exponent is multiplied by -1. Multiplying x by -1 implies the reflection of the graph across y-axis.
The function value is multiplied by 3. This suggest a vertical expansion by a factor of 3.
2 is being added to the function value, this implies a vertical shift upwards by 2 units.
So, we can write:
y = g(x) = 3f(-x) + 2
Thus following translations are applied:
a) Reflection across y-axis
b) Vertical stretch by a factor of 3
c) Upward shift by 2 units
We have to explain how the given function can be obtained from the parent function.
Let y=g(x)
So,
Notice that x in the exponent is multiplied by -1. Multiplying x by -1 implies the reflection of the graph across y-axis.
The function value is multiplied by 3. This suggest a vertical expansion by a factor of 3.
2 is being added to the function value, this implies a vertical shift upwards by 2 units.
So, we can write:
y = g(x) = 3f(-x) + 2
Thus following translations are applied:
a) Reflection across y-axis
b) Vertical stretch by a factor of 3
c) Upward shift by 2 units