Write down the coordinates of U - NSC Mathematics - Question 4 - 2017 - Paper 1

The equations of the asymptotes of g are:

• Vertical asymptote: $x = 1$
• Horizontal asymptote: $y = 1$

T is located at the point where the graphs intersect the x-axis. From the graph, the coordinates of T are determined to be (-1, 0).

The function h(x) is the reflection of f(x) in the line y = x. Since $f(x) = ext{log}_a(x)$, then the reflection gives: $h(y) = ext{log}_a(y)$ o or [y = a^x] where y is expressed in terms of x.

The asymptote of h(x) is found by observing the behavior as x approaches the vertical asymptote. Therefore, the asymptote of h(x-3) remains unchanged and is given by: $x = 3$.

V is located based on where the asymptotes of g intersect the line y = x. The coordinates of V are calculated as: $V(\sqrt{2} + 1, \sqrt{2} + 1)$.

To find the coordinates of T', we reflect T around R. Given T(-1, 0) and R(2, 2), we can calculate T'. The coordinates of T' are (3, 4).