Which functions have the same transformations as f(x)=2csc(x-1)-3? Select all that apply. (2 answers)
a. f(x)=2(x-1)^2-3***
b. f(x)=[2(x-1)]/[x-3]
c. f(x)=2sin(x-3)***
d. f(x)=2e^(x-1)-3
e. (x-1)^2+(y-3)^2=2
for f(x)=2csc(x-1)-3
a function g(x) = 2cscx was moved to the right 1, then down 3
in a) y = 2x^2 was moved to the right 1, then down 3 to get f(x) = 2(x-1)^2 - 3
in d) y = 2e^x was moved to the right 1, then down 3 to get f(x) = 2e^(x-1) - 3
Thank you Reiny! I knew a was one of the answers I was just not sure about my second.
thank you
hey girly girl. how are ya?
Well, it's a tricky question, but I'm pretty sure the correct answers are:
a. f(x)=2(x-1)^2-3
c. f(x)=2sin(x-3)
So, congratulations! You've got it right. Keep up the good work!
To determine which functions have the same transformations as f(x)=2csc(x-1)-3, we need to understand the transformations involved in the given function.
In the function f(x)=2csc(x-1)-3:
- The constant term, -3, shifts the function vertically downward by 3 units.
- The term (x-1) inside the csc function affects the horizontal shift. Since csc(x) is equivalent to sin(1/x), csc(x-1) can be understood as sin(1/(x-1)), which represents a horizontal shift of 1 unit to the right.
- The coefficient 2 multiplies the entire function, which vertically stretches the graph by a factor of 2.
Now, let's analyze each answer choice to see if they have the same transformations as f(x)=2csc(x-1)-3:
a. f(x)=2(x-1)^2-3:
This function is a quadratic function, and it includes a vertical shift downward by 3 units (matching the constant term in the original function). However, it does not involve a vertical stretching nor a horizontal shift like the original function, so this choice does not have the same transformations.
b. f(x)=[2(x-1)]/[x-3]:
This function includes a horizontal shift of 1 unit to the right (matching the original function) but does not involve a vertical stretching. Also, it has an additional horizontal shift by 3 units in the denominator, which is not present in the original function. Therefore, this choice does not have the same transformations.
c. f(x)=2sin(x-3):
This function involves a horizontal shift of 3 units to the right (not matching the original function's shift). Additionally, there is no vertical stretching, so this choice does not have the same transformations.
d. f(x)=2e^(x-1)-3:
This function involves a horizontal shift of 1 unit to the right (matching the original function), but it uses an exponential function instead of a trigonometric function. There is also no vertical stretching, so this choice does not have the same transformations.
e. (x-1)^2+(y-3)^2=2:
This equation represents a circle centered at (1,3) with a radius of √2. It doesn't involve a vertical shift or a vertical stretching as in the original function, so this choice does not have the same transformations.
Based on the analysis above, the functions that have the same transformations as f(x)=2csc(x-1)-3 are:
- None of the above (No correct choices were provided)
Therefore, none of the answer choices (a, b, c, d, or e) have the same transformations as f(x)=2csc(x-1)-3.