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kirill [66]
3 years ago
9

Which of the following rational functions is graphed below?

Mathematics
1 answer:
IrinaVladis [17]3 years ago
6 0

Answer:

Option (D)

Step-by-step explanation:

The given graph represents a rational function having,

1). Vertical asymptote → x = 2

2). Horizontal asymptote → y = 0

Parent function representing the rational function will be in the form of,

F(x) = \frac{1}{x^{2} }

Since, vertical asymptote of the function is x = 2, denominator of the function will be in the form of (x - 2)².

Since, horizontal asymptote of the function is y = 0, highest exponent term in the numerator will be 0.

Therefore, numerator of the fraction will be x⁰.

The rational function given in the graph will be,

F(x) = \frac{x^{0}}{(x-2)^2}

F(x) = \frac{1}{(x-2)^2}

Option (D) will be the answer.

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Which set represents the same relation as the graph below?<br><br> A<br> B<br> C<br> D
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B. {( -1,-2 ), ( -3,-2 ), ( -5,4 ), ( 2,0 ), ( 3,3 ), ( 4,5 ), ( 6,-4 )}

Step-by-step explanation:

We are given the graph showing the points of a relation.

According to the graph, we see that, the given points of the relation are:

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As, we see that there are 7 points in the relation.

So, option C and D are not correct as they have 5 and 6 points respectively.

Also, option A is wrong as it contains different set of points.

Hence, we get that option B is correct.

That is the set representing the graphed relation is {( -1,-2 ), ( -3,-2 ), ( -5,4 ), ( 2,0 ), ( 3,3 ), ( 4,5 ), ( 6,-4 )}

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What are the coordinates of the endpoints of the midsegment for △DEF that is parallel to DE¯¯¯¯¯?
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Answer:

The endpoints of the midsegment for △DEF that is parallel to DE, are (-1,3.5) and (-1,2).

Step-by-step explanation:

If a line connecting the midpoint of two sides and parallel to the third side of the triangle, then it is called a midsegment.

From the given figure it is noticed that the vertices of the triangle are D(1,4), E(1,1) and F(-3,3).

If the midsegment is parallel to DE, then the end points of the midsegment are mid point of DF and EF.

Midpoint formula.

Midpoint=(\frac{x_1+x_2}{2},\frac{y_1+y_2}{2})

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Midpoint=(\frac{1-3}{2},\frac{4+3}{2})

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Midpoint of EF,

Midpoint=(\frac{1-3}{2},\frac{1+3}{2})

Midpoint=(-1,2)

Therefore the endpoints of the midsegment for △DEF that is parallel to DE, are (-1,3.5) and (-1,2).

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