Question

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

Answer 1

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 \(\displaystyle{\left({0},-{\frac{{{6}}}{{{7}}}}\right)}\)