.In the function f(x), x is replaced with 2x and 1 is added to the function.
f(x)=−3sinx
What effect does this have on the graph of the function?
a. The graph is horizontally compressed by a factor of 2 and shifts up 1 unit
b. The graph is horizontally compressed by a factor of 2 and shifts down 1 unit
c. The graph is vertically stretched by a factor of 2 and shifts up 1 unit*
d. The graph is vertically stretched by a factor of 2 and shifts down 1 unit
To determine the effect of replacing x with 2x and adding 1 to the function f(x) = -3sinx, let's break it down step-by-step:
Step 1: Replacing x with 2x
When we replace x with 2x, we end up with f(2x) = -3sin(2x). This means that every x-coordinate on the graph is multiplied by 2.
Step 2: Adding 1 to the function
After adding 1 to the function, we have f(2x) + 1 = -3sin(2x) + 1. This means that after multiplying every x-coordinate by 2, we also shift the graph up 1 unit.
Combining both transformations, we conclude that the graph of the function is horizontally compressed by a factor of 2 and vertically shifted up by 1 unit. Therefore, the correct answer is:
a. The graph is horizontally compressed by a factor of 2 and shifts up 1 unit.
To determine the effect on the graph, let's break down the given transformations.
The function \( f(x) \) is given as \( -3\sin(x) \). This is a standard sine function with an amplitude of 3 and no horizontal or vertical shifts.
Now let's look at the given transformations:
1. \( x \) is replaced with \( 2x \). This means that the x-values are multiplied by 2, which has the effect of horizontal compression. Instead of the period of the sine function being \( 2\pi \), it will now be \( \frac{2\pi}{2} = \pi \).
2. 1 is added to the function. This means that the entire graph will shift vertically upward by 1 unit.
Combining these transformations, we can conclude that the correct answer is option c. The graph is vertically stretched by a factor of 2 (amplitude becomes 6) and shifts up 1 unit.
Ok. So B??
No
I suggest making a quick sketch of
y = -3sinx
and
y = -3sin(2x) + 1
pick critical angles like 30, 45, 60, 90 degrees etc