# Find the x-and y-intercepts of the rational function f(x)=\frac{6}{x^{2}+4x-7}

Question
Upper level algebra
Find the x-and y-intercepts of the rational function
$$\displaystyle{f{{\left({x}\right)}}}={\frac{{{6}}}{{{x}^{{{2}}}+{4}{x}-{7}}}}$$

2021-01-09
As x -intercept is a point on the graph where $$\displaystyle{y}={0}$$,
$$\displaystyle{\frac{{{6}}}{{{x}^{{{2}}}+{4}{x}-{7}}}}={0}$$ implies there is no solution for $$\displaystyle{x}\in{R}$$.
$$\displaystyle\therefore$$ There is no x -intercept point.
As y -intercept is a point on the graph where $$\displaystyle{x}={0}$$,
$$\displaystyle{y}={\frac{{{6}}}{{{0}^{{{2}}}+{4}{\left({0}\right)}-{7}}}}$$
$$\displaystyle{y}=-{\frac{{{6}}}{{{7}}}}$$ $$\displaystyle\therefore$$ y-intercept is $$\displaystyle{\left({0},-{\frac{{{6}}}{{{7}}}}\right)}$$

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