Respuesta :
The parent function for this function is
[tex]f(x)= 7^{x} [/tex]
We have to explain how the given function can be obtained from the parent function.
Let y=g(x)
So,
[tex]g(x)=3*7^{-x} +2[/tex]
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
[tex]f(x)= 7^{x} [/tex]
We have to explain how the given function can be obtained from the parent function.
Let y=g(x)
So,
[tex]g(x)=3*7^{-x} +2[/tex]
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
Answer:
Sketch the graph of y= 7^x
Reflect the graph across the y-axis to show the function y= 7^-x
Stretch the graph vertically by a factor of 3 to show the function y= 3⋅7^-x
Shift the graph up 2 units to show the function y= 3 ⋅ 7^-x +2
