Which of the following are attributes of the function f(x)= |4(x-8)|-1 ?
2 answers:
Answer:
Option 1 and 2.
Step-by-step explanation:
Given : Function
To find : Which of the following are attributes of the function?
Solution :
We find the domain, range , x-intercept and symmetry of the given function to match from given attributes.
Function
1) Domain is defined as the set of values in which function is defined.
Since, The given function for value x is under the absolute function so it is defined for all real numbers.
i.e.
2) The range is defined as the set of values that correspond with the domain.
i.e.
3) x - intercept is defined as the value of x when y=0.
So,
The values of x are
So, x-intercept exist.
4) Symmetry about x-axis
We show it by graphically as the vertex of equation is (8,0)
And if we construct a line x=8 the graph divides into two equal parts which means it is symmetrical at x=8.
Refer the attached figure below.
Therefore, From the following options, Option 1 and 2 are correct.
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The graph can be drawn by the placing the points and after translation points becomes A'(-3, -5), B'(-2, 3), C'(1, 4), and D'(0, -5)
<h3>What is quadrilateral?</h3>It is defined as the four-sided polygon in geometry having four edges and four corners.
We have:
Quadrilateral ABCD with vertices A(2,-3), B(3,5), C(6,6) and D(5,-3)
We can graph it on the coordinate plane as shown in the picture.
After applying the translation (x, y)→(x−5, y−2), the points becomes:
A'(-3, -5)
B'(-2, 3)
C'(1, 4)
D'(0, -5)
Similarly, we can graph it on the coordinate plane (refer attached picture)
Thus, the graph can be drawn by the placing the points and after translation points becomes A'(-3, -5), B'(-2, 3), C'(1, 4), and D'(0, -5)
Learn more about the quadrilateral here:
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These are a huge pain. First set up your initial triangle with A and B as your base angles and C as your vertex angle. Now drop an altitude and call it h. You need to solve for h. Use sin 56 = h/13 to get that h = 10.8. The rule is that if the side length of a is greater than the height but less than the side length of b, you have 2 triangles. h<a<b --> 10.8<12<13. Those are true statements so we have 2 triangles. Side a is the side that swings, this is the one we "move", forming the second triangle. First we have to solve the first triangle using the Law of Sines, then we can solve the second. 
to get that angle B is 64 degrees. Now find C: 180-56-64=60. And now for side c: 
and c=12.5. That's your first triangle. In the second triangle, side a is the swinging side and that length doesn't change. Neither does the angle measure. Angle B has a supplement of 180-64 which is 116. So the new angle B in the second triangle is 116, but the length of b doesn't change, either. I'll show you how you know you're right about that in just a sec. The only angle AND side that both change are C and c. If our new triangle has angles 56 and 116, then C has to be 8 degrees. Using the Law of Sines again, we can solve for c:
and c = 2.0. We can look at this new triangle and determine the side measures are correct because the longest side will always be across from the largest angle, and the shortest side will always be across from the smallest angle. The new angle B is 116, which is across from the longest side of 13. These are hard. Ugh.