Answer:
[tex]g(x)=(1.6)^{x-9}+5[/tex]
Step-by-step explanation:
Given: [tex]f(x)=(1.6)^x[/tex]
The given function is [tex]f(x)=(1.6)^x[/tex].
It is exponential function because x as power of 1.6.
For left / right shift : change in x value
- For right [tex]x\rightarrow x-a[/tex]
- For left [tex]x\rightarrow x+a[/tex]
For up / down shift : change in f(x)
- For up [tex]f(x)\rightarrow f(x)+a[/tex]
- For down [tex]f(x)\rightarrow f(x)-a[/tex]
[tex]f(x)=(1.6)^x[/tex]
Shift up 5 units
[tex]g(x)=f(x)+5[/tex]
Shift 9 unit right
[tex]g(x)=f(x-9)+5[/tex]
[tex]g(x)=1.6^{x-9}+5[/tex]
Hence, The new function will be [tex]g(x)=(1.6)^{x-9}+5[/tex]
