Answer:
The image of the graph of the function f(x) = sin(x + π/2) is given below.
Explanation:
The graph of the function f(x) = sin(x + π/2) is a sine wave that is shifted π/2 units to the left.
This can be seen by analyzing the graph of the parent function
f(x) = sin(x) and considering the effect of the phase shift.
The parent function f(x) = sin(x) oscillates between -1 and 1, with period 2π.
It passes through the origin at points (π/2, 1), (3π/2, -1), (5π/2, 1), and so on.
To find the graph of f(x) = sin(x + π/2), we shift the graph of f(x) = sin(x) π/2 units to the left.
This means that the graph of f(x) = sin(x + π/2) will pass through the origin at points (π/4, 1), (3π/4, -1), (5π/4, 1), and so on.
Thus,
The image of the graph of the function f(x) = sin(x + π/2) is given below.
Question:
What does the graph of the function f(x) = sin(x + π/2) look like?