<ol class="i-list"><li><div class="list-item-paragraph">Describe a sequence of transformations which transforms the graph of $y=\frac{1}{x}$ to the graph of $y=\frac{3x+5}{x+2}$.</div><p style="text-align: right;">[2]</p></li><li><div class="list-item-paragraph">Sketch the graphs of $y=\frac{3x+5}{x+2}$ and $16{{\left( x+3 \right)}^{2}}+9{{\left( y-4 \right)}^{2}}=144$ on a single diagram, indicating clearly any axial intercepts, points of intersection of the two graphs and the equations of asymptotes.</div><p style="text-align: right;">[5]</p></li><li><div class="list-item-paragraph">Hence find the set of values of $x$ that satisfies the inequality $\frac{3x+5}{x+2}>4-\sqrt{\frac{144-16{{\left( x+3 \right)}^{2}}}{9}}$.</div><p style="text-align: right;">[2]</p></li></ol>

Describe a sequence of transformations which transforms the graph of $y=\frac{1}{x}$ to the graph of $y=\frac{3x+5}{x+2}$.

Sketch the graphs of $y=\frac{3x+5}{x+2}$ and $16{{\left( x+3 \right)}^{2}}+9{{\left( y-4 \right)}^{2}}=144$ on a single diagram, indicating clearly any axial intercepts, points of intersection of the two graphs and the equations of asymptotes.

Hence find the set of values of $x$ that satisfies the inequality $\frac{3x+5}{x+2}>4-\sqrt{\frac{144-16{{\left( x+3 \right)}^{2}}}{9}}$.

2019 HCI Promo Q10

2019 HCI Promo Q10

Video Solution:

Solution:

Solution locked