which transformation is not in this function? f(x) = sinx to g(x) = −2 sin (3x−120) −8
A horizontal compression by a factor of 3
A phase shift of 120 to the right
A reflection in the x-axis
A vertical shift 8 unit downwards
B (why?)
because x has to be 40 before it reaches the old zero :)
To identify the transformations in the given function, we need to understand the effects of each transformation on the parent function f(x) = sin(x). Let's analyze each option:
1. A horizontal compression by a factor of 3:
The general form for a horizontal compression is f(ax), where a is the compression factor. In this case, if we compare f(x) = sin(x) with g(x) = -2sin(3x - 120) - 8, we notice that the 3 in front of the x is a horizontal compression by a factor of 3. Therefore, this transformation is present in g(x).
2. A phase shift of 120 to the right:
The general form for a phase shift to the right is f(x - b), where b is the amount of the shift. In this case, comparing f(x) = sin(x) with g(x) = -2sin(3x - 120) - 8, we can observe that the -120 inside the sin function causes a phase shift of 120 degrees to the right. Hence, this transformation is present in g(x).
3. A reflection in the x-axis:
A reflection in the x-axis occurs when the function is multiplied by -1. In this case, comparing f(x) = sin(x) with g(x) = -2sin(3x - 120) - 8, we see that the -2 in front of sin(x) reflects the graph in the x-axis. Hence, this transformation is present in g(x).
4. A vertical shift 8 units downward:
A vertical shift occurs when a constant is added or subtracted to the function. In this case, comparing f(x) = sin(x) with g(x) = -2sin(3x - 120) - 8, we can see that the -8 at the end of g(x) causes a vertical shift of 8 units downward. Therefore, this transformation is present in g(x).
Based on the analysis above, all the mentioned transformations are present in the function g(x) = -2sin(3x - 120) - 8. Therefore, none of the options are correct, as all transformations are present in the given function.