Please help me! I'm spending 50 points on this question and my last two questions never even got answered!
1 answer:
Answer:
C.
Step-by-step explanation:
Domain is only affected if certain values can make the result something that either doesn't make sense or is an error. In your situation, it wants you to find the domain of f/g, which is a fraction. The only rule we have for fractions regarding domain is that we simply can't divide by zero, to find the domain for any fraction with variables in the denominator, what I do is take the denominator, set it equal to 0, and solve for x.
So, if we're taking f/g, we have:
4x - 3 makes up our denominator, the bottom part of the fraction. So
4x - 3 = 0
4x = 3
x = 3/4
So the denominator is equal to zero when x is equal to 3/4. This would produce an error in any calculator because you can't divide by zero. The domain here is all real numbers except for 3/4.
(For future problems, the only thing to look out for is if your numerator, the top part of the fraction, factors into something that cancels with the bottom. In that case, it wouldn't affect domain because you aren't actually dividing by anything. For example:
If we factor the top, we see that x^2 - 4 = (x - 2)(x + 2). In this case, we have (x - 2) in both the top and bottom of the fraction, so it cancels out, and from there nothing else is restricting our domain. It would be all real numbers in a case like that.)
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Answer:
1. Translation: g(x) = f(x-a)+b.
2. Reflection around y-axis: h(x) = f(-x)
3. Reflection around x-axis: k(x) = -f(x)
4. Rotation of 90° :
5. Rotation of 180° : .
6. Rotation of 270° : .
Step-by-step explanation:
Let us assume that the transformations namely translation, reflection are applied to a function f(x) and the rotation is applied to the point ( x,y ).
So, according to the options:
We know that 'translation moves the image in horizontal and vertical direction'.
1. As we have to translate the function f(x) 'a' units to the right and 'b' units up. So, the new form of the function becomes g(x) = f(x-a)+b.
Further, we know that 'reflection means to flip the image around a line'.
2. As, we have to reflect the function f(x) around y-axis. The new form of the function is h(x) = f(-x).
3. As, we have to reflect the function f(x) around x-axis. The new form of the function is k(x) = -f(x).
Since, 'rotation turns the image around a point to a certain degree'.
4. As, we have to rotate ( x,y ) counter-clockwise to 90° about the origin, the new form of the function is .
5. As, we have to rotate ( x,y ) counter-clockwise to 180° about the origin, the new form of the function is .
6. As, we have to rotate ( x,y ) counter-clockwise to 270° about the origin, the new form of the function is .