select the correct answer. consider function g where function f is the parent sine function. g(x)=f(x - π/3)…
select the correct answer. consider function g where function f is the parent sine function. g(x)=f(x - π/3) how will the graph of function g differ from the graph of function f? a. the graph of function g is the graph of function f shifted π/3 units to the left. b. the graph of function g is the graph of function f shifted 3 units up. c. the graph of function g is the graph of function f shifted 3 units down. d. the graph of function g is the graph of function f shifted π/3 units to the right.
Answer
Explanation:
Step1: Recall function - shift rule
For a function $y = f(x - h)$, the graph of $y = f(x)$ is shifted $h$ units to the right when $h>0$ and $|h|$ units to the left when $h < 0$.
Step2: Identify the value of $h$
In the function $g(x)=f(x-\frac{\pi}{3})$, we have $h = \frac{\pi}{3}>0$.
Answer:
D. The graph of function $g$ is the graph of function $f$ shifted $\frac{\pi}{3}$ units to the right.