ANSWER
EXPLANATION
We want to find the absolute value function for the line in blue.
The general form of an absolute value function is:
where (h, k) = vertex
From the line, the vertex of the graph in blue is:
To find a, we have to pick a point (x, y) on the line and input it into the general function.
Let us pick (2, 1).
Therefore, we have:
Therefore, the absolute value function is:
<h3>Answer: Choice D</h3>
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Explanation:
The long way to do this is to multiply all the fractions out by hand, or use a calculator to make shorter work of this.
The shortest way is to simply count how many negative signs each expression has.
The rule is: if there are an even number of negative signs, then the product will be positive. Otherwise, the product is negative.
For choice A, we have 3 negative signs. The result (whatever number it is) is negative. Choice B is a similar story. Choice C is also negative because we have 1 negative sign. Choices A through C have an odd number of negative signs.
Only choice D has an even number of negative signs. The two negatives multiply to cancel to a positive. The negative is like undoing the positive. So two negatives just undo each other. This is why the multiplied version of choice D will be some positive number.
Or you can think of it as opposites. If you are looking up (positive direction) and say "do the opposite" then you must look down (negative direction). Then if you say "do the opposite", then you must look back up in the positive direction.
Answer:
Step-by-step explanation:
What did you include in your response? Check all that apply.
There would be an open circle at (2, 1). <u>Yes</u>
There would be a closed circle at (2, 3). <u>Yes</u>
There would be an open circle at (4, 3). <u>Yes</u>
There would be a closed circle at (4, −4). <u>Yes</u>
Endpoints that are not included in the domain of a particular piece of a function are represented by an open circle. <u>Yes</u>
It would be 0.81 because she got 81/100 right. Hope this helpz..
Answer:
absolute max is 120 and absolute min is -8
Step-by-step explanation:
Find critical numbers
f'(x) = 3x^2 - 12x + 9 = 0
= 3(x^2 - 4x + 3) = 0
3(x-3)(x-1) = 0
(x-3) = 0 or (x-1)=0
x = 1,3
Test them!
x<1 Sign of f' on this interval is positive
1<x<3 Sign of f' on this interval is negative
x>3 Sign of f' on this interval is positive
f(x) changes from positive to negative at x = 1 which means there is a relative maximum here.
f(x) changes from negative to positive at x = 3 which means there is a relative minimum here.
Test the endpoints to find the absolute max and min.
f(-1) = -8
f(1) = 12
f(3) = 8
f(7) = 120
The absolute maximum value of f is 120 and the absolute minimum value of f is -8.
