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Sauron [17]
1 year ago
11

Which point lies on the graph of y = 2?A. (1.2)B. (1-2)C. (2, 18)D.(3, 2)

Mathematics
1 answer:
irinina [24]1 year ago
3 0

A garph y=2 represents a line parallel to the x axis with the y coordinate equal to 2.

The point which lies on the y=2 graph has its y coordinate equal to 2.

In the given options, (3,2) is the coordinate with the y coordinate equal to 2.

Hence, (3,2) lies on the graph of y = 2.

Option (D) is the answer.

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Can someone help me with this? I need to find the points of discontinuity/limits for each of these. I think one point is 4, but
Debora [2.8K]
The answers are shown in the attached image

-------------------------------------------------------------------------

Explanation:

Set the denominator x^4-8x^3+16x^2 equal to zero and solve for x

x^4-8x^3+16x^2 = 0
x^2(x^2-8x+16) = 0
x^2(x-4)^2 = 0
x^2 = 0 or (x-4)^2 = 0
x = 0 or x-4 = 0
x = 0 or x = 4

The x values 0 and 4 make the denominator zero

These x values lead to asymptote discontinuities because the numerator 8x-24 = 8(x-3) has no common factors which cancel with the denominator factors.

There are two vertical asymptotes

Let's see what happens when we plug in a value to the left of x = 0, say x = -1, we'd get
f(x) = (8x-24)/(x^4-8x^3+16x^2)
f(-1) = (8(-1)-24)/((-1)^4-8(-1)^3+16(-1)^2)
f(-1) = -1.28
So as x gets closer and closer to x = 0 from the left side, the f(x) is heading to negative infinity

Now plug in some value to the right of x = 0. I'm going to pick x = 1
f(x) = (8x-24)/(x^4-8x^3+16x^2)
f(1) = (8(1)-24)/((1)^4-8(1)^3+16(1)^2)
f(1) = -1.78 (approximate)
So as x gets closer and closer to x = 0 from the right side, the f(x) is heading to negative infinity

Overall, as x approaches 0 from either the left or right side of x = 0, the y value is heading off to negative infinity

---------------------

Repeat for values to the left and right of x = 4
We can't use x = 1 as it turns out that x = 3 is a root
But we can use something like x = 3.5 to find that...
f(x) = (8x-24)/(x^4-8x^3+16x^2)
f(3.5) = (8(3.5)-24)/((3.5)^4-8(3.5)^3+16(3.5)^2)
f(3.5) = 1.31 approx
So as x gets closer to x = 4 from the left, y is getting closer to positive infinity

Plug in x = 5 to find that
f(x) = (8x-24)/(x^4-8x^3+16x^2)
f(5) = (8(5)-24)/((5)^4-8(5)^3+16(5)^2)
f(5) = 0.64
which has the same behavior as the left side

So overall, as we approach x = 4, the y value is heading off to positive infinity

Again everything is summarized in the image attachment

Note: you could make a table of more values but they would effectively say what has already been said. It would be redundant busy work. However, its always good practice for function evaluation. 

6 0
3 years ago
How to solve 7 2/6 + 8 5/6
natima [27]
Separate them first.
7+8=15
5/6+2/6=7/6
There can't be 7/6, so it becomes 1 and 1/6,
15+1+1/6=16 1/6
The answer is 16 1/6.
3 0
3 years ago
Is 1/8 x 4= 1/12 or 4/8
aliina [53]

Answer:

If you were to fully simplify it would technically be 1/2 as 4/8 is correct but can be further rounded down

Step-by-step explanation:

1/8 x 4 = 4/8

4/8 ÷ 4 = 1/2

5 0
2 years ago
Read 2 more answers
Please help me please i really neeed help
777dan777 [17]

Answer:

A: positive B: Negative C: Positive

Step-by-step explanation:

4 0
3 years ago
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Write the equations after translating the graph of y = | 1/2x−2|+3, one unit to the right
AveGali [126]

y=|\dfrac{1}{2}x-2|+3

Since we are translating this graph one unit to the right, replace x with (x-1)

Note: If you are translating a graph to the left by k units, replace x with (x+k), and if by the right, replace x with (x-k)

y=|\dfrac{1}{2}(x-1)-2|+3

After simplifying, we now have the following equation:

=|\dfrac{1}{2}x-\dfrac{5}{2}|+3

This is the new equation. Let me know if you need any clarifications, thanks!

6 0
3 years ago
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