which functions have the same transformations as f(x)=3csc(x+6)-4? select all that apply
f(x)= 3(x+6)/x-4
f(x)=(3e^x+6)-4
f(x)=3sin(x+4)
f(x)=3(x+6)^2)-4
(x+6)^2+(y-4)^2=3
B) f(x) = 3e^(x+6)-4
and
D) f(x) = 3(x+6)^2-4
Well, I must say, these transformations are quite the jokers! Let's see which functions have the same transformations as f(x)=3csc(x+6)-4:
1. f(x) = 3(x+6)/x-4: Sorry, but this function is not quite a match for f(x)=3csc(x+6)-4. It looks like this function involves some division and substitution, which is not what our original function is doing.
2. f(x) = (3e^x+6)-4: Nope, this function also doesn't have the same transformations as f(x)=3csc(x+6)-4. Here we have some exponential action going on with e^x, which is not present in our original function.
3. f(x) = 3sin(x+4): Ah, seems like we have a winner! This function does indeed have the same transformations as f(x)=3csc(x+6)-4. The only difference is that we have sin(x+4) instead of csc(x+6), but otherwise, the transformations are a perfect match.
4. f(x) = 3(x+6)^2)-4: Nope, sorry, this function is not a match. It looks like we have a quadratic function here, with a squared term, which is not present in our original function.
5. (x+6)^2+(y-4)^2=3: Haha, this one is a little off-topic. It looks like we have an equation of a circle here, which is definitely not the same as our original function f(x)=3csc(x+6)-4.
So, the only function that has the same transformations as f(x)=3csc(x+6)-4 is f(x) = 3sin(x+4). Keep on joking!
To determine which functions have the same transformations as f(x) = 3csc(x+6) - 4, we need to consider the properties of the given function.
First, let's break down the given function f(x) = 3csc(x+6) - 4:
1. The coefficient 3 in front of csc(x+6) affects the vertical scaling of the graph.
2. The "x+6" inside the csc function affects the horizontal translation (shifting) of the graph.
3. The constant term -4 affects the vertical translation (shifting) of the graph.
Now, let's analyze each given function:
1. f(x) = 3(x+6)/(x-4)
This function involves a rational expression instead of a trigonometric function. It does not have the same form as f(x) = 3csc(x+6) - 4, so it does not have the same transformations.
2. f(x) = (3e^x + 6) - 4
This function involves the exponential function e^x and does not include a csc function. It also does not have the same form as f(x) = 3csc(x+6) - 4, so it does not have the same transformations.
3. f(x) = 3sin(x+4)
This function involves the sine function instead of the cosecant function (csc). However, the form of this function is the same as f(x) = 3csc(x+6) - 4 with similar transformations, except for the horizontal translation of 2 units (compare x+4 and x+6). Therefore, this function has the same transformations as f(x) = 3csc(x+6) - 4.
4. f(x) = 3(x+6)^2 - 4
This is a quadratic function involving (x+6)^2 instead of a trigonometric function. It does not have the same form as f(x) = 3csc(x+6) - 4, so it does not have the same transformations.
5. (x+6)^2 + (y-4)^2 = 3
This is the equation of a circle, not a function. It does not have the same form as f(x) = 3csc(x+6) - 4, so it does not have the same transformations.
In summary, only f(x) = 3sin(x+4) has the same transformations as f(x) = 3csc(x+6) - 4.
you might want to include the vertical scaling by a factor of 3, as well, though it does not affect the answer.
f(x)=3csc(x+6)-4
is a translation of g(x) = 3csc x of 6 units to the left and 4 units down
f(x)=3(x+6)^2)-4
is a translation of k(x) = 3x^2 of 6 units to the left, and 4 units down