The rational function graphed is determined by the asymptotes and the
intercepts of the graph.
Response:
The rational function that is graphed is option D;
[tex]D. \hspace{0.15 cm} F(x) = \dfrac{x}{(x + 4) \cdot (x - 1)}[/tex]
How can the function represented by the graph be found?
The given graph has vertical asymptote at x = -4, and x = 1
Therefore;
- Factors in the denominator includes (x + 4), and (x - 1)
From the graph, at x = 0, F(x) = 0, which gives;
- A factor of the numerator is; x
Between -4 < x < 1, as the x-value increases, F(x) decreases more
rapidly, which gives;
The power of the polynomial in the denominator is larger than the numerator and is an even number.
The function is therefore;
[tex]\underline{D. \hspace{0.15 cm} F(x) = \dfrac{x}{(x + 4) \cdot (x - 1)}}[/tex]
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