What effect does changing the function
f(x)=2sin(x2)−1 to the function
g(x)=2sin(x)−5 have on the graph of f(x)?
The graph is stretched vertically by a factor of 2 and shifted right 4 units .
The graph is compressed vertically by a factor of 2 and shifted left 4 units .
The graph is compressed horizontally by a factor of 2 and shifted down 4 units.
The graph is stretched horizontally by a factor of 2 and shifted up 4 units .
My answer is C
I'm so sorry!! I actaully meant f(x)=2sin(x/2)-1
Your answer is correct. The effect of changing the function f(x)=2sin(x^2)-1 to the function g(x)=2sin(x)-5 is that the graph is compressed vertically by a factor of 2 and shifted down 4 units. So, option C is the correct answer.
To determine the effect of changing the function f(x) = 2sin(x^2) - 1 to the function g(x) = 2sin(x) - 5 on the graph of f(x), we need to analyze the changes made to the original function.
Let's break down the changes one by one:
1. 2sin(x^2) - 1 vs. 2sin(x) - 5:
- The first change is the replacement of x^2 with x. This change compresses the graph horizontally by a factor of 2.
- The second change is the replacement of the constant term -1 with -5. This shift the graph downwards by 4 units.
Since the first change affects the horizontal direction and the second change affects the vertical direction, we can conclude that the graph is:
- Compressed horizontally by a factor of 2 (which corresponds to the graph being stretched horizontally by a factor of 1/2).
- Shifted downwards by 4 units.
Therefore, your answer, option C, is correct.
The graph is compressed horizontally by a factor of 2 and shifted down 4 units.
assuming you meant f(x) = 2sin(x^2) - 1
look at the graphs of these two:
http://www.wolframalpha.com/input/?i=plot+y%3D2sin(x%5E2)%E2%88%921+,+y%3D2sin(x)%E2%88%925
none of the given answers are correct.
The problem is the x ---> x^2
There is compression, but at an accelerated rate for |x|?1
All your choices have the compression by a factor of 2
looking at the constants at the end, there is a vertical shift down 4 units, one of the choices has that