Answer:
A,C and D
Step-by-step explanation:
We are given that
\(f(x)=3(4)^{x-5}+\frac{2}{3}\)
We have to find the graph of given function relate to its parent function.
Let parent function
\(g(x)=4^x\)
Now, the graph shift 5 unit towards right by the rule of transformation
\(g(x)\rightarrow g(x-5)\)
Therefore, by using this rule then, we get
\(g(x)=(4)^{x-5}\)
Now, stretch vertically 3 times the previous graph by using the rule of transformation
\(f(x)\rightarrow 3f(x)\)
Now, after applying this rule we get
\(g(x)=3(4)^{x-5 }\)
Now, shift the graph \(\frac{2}{3}\) unit upward by the rule of transformation
\(f(x)\rightarrow f(x)+\frac{2}{3}\)
After applying this rule then, we get
\(f(x)=3(4)^{x-5}+\frac{2}{3}\)
Hence, options A ,C and D are true.
