Given:
Parent function is [tex]f(x)=5^x[/tex].
New function is [tex]y=-2(5)^{3x}+8[/tex].
To find:
The equation of function after each transformation.
Solution:
We have,
[tex]f(x)=5^x[/tex]
The equation of parent function is
[tex]y=5^x[/tex]
1. [tex]y=5^{3x}[/tex] (Horizontal compression by factor 3)
2. [tex]y=2(5)^{3x}[/tex] (Vertical stretch by factor 2)
3. [tex]y=-2(5)^{3x}[/tex] (Reflected across x-axis)
4. [tex]y=-2(5)^{3x}+8[/tex] (Shift 8 units above)
Therefore, these are the required answers.
