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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Please help... need help ASAP due today... which ones are the answers?

andrey2020 [161]

Answer:

Choices 1 and 4 are correct.

Step-by-step explanation:

We first need to find what the slope of the line is. That way, we can find out which possible answers are perpendicular to it:

$\frac{4-(-2)}{3-1}=\frac{6}{2}=3$

Since we now have the slope, we need the negative reciprocal of it. Remember: if x is the slope, it's negative reciprocal will be $-\frac{1}{x}$ . Therefore, if the line's slope is 3, then we need to find answers with a slope of $-\frac{1}{3}$ .

The first answer is correct, as you have marked. The second answer, while written a little weirdly, does show the slope as 3, which we know as wrong. The third choice is not correct, however. This equation is written in point-slope form, where $y-y_{1}=m(x-x_{1})$ . The only variable we have to worry about is m, which, in the third choice, is 3. The fourth answer is correct, which sounds weird at first. Let's put that equation into slope-intercept form: