# Maths Paper 1, November 2024, question 5.5

> The function f is given in the information above. Graph f is transformed to a new... Marked mark by mark. Q5.5, Maths Paper 1 November 2024, 2 marks.

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Last updated: 2026-11-12

Subject: Maths. Source: Based on Nov 2024 · Paper 1 · Q5.5. Marks: 2. Not yet checked by a teacher.

## Question 5.5 (2 marks)

$f(x)=\frac{a}{x+p}+q$ has domain $x\neq 2$. Its vertical asymptote is $x=2$ and its graph cuts the $y$-axis at $(0;1)$. The line $g(x)=x-3$ is a line of symmetry of $f$. Each branch of $f$ is increasing, and $f(x)=-\frac{4}{x-2}-1$.

The function $f$ is given in the information above. Graph $f$ is transformed to a new graph $h$ so that:
• $h$ has the same domain and the same range as $f$
• the gradient of $h$ is negative at every point of its domain, that is $h’(x).
Describe one possible transformation of $f$ that gives $h$.

Figure: Graph of a hyperbola f with a vertical dashed asymptote x = 2 and a horizontal dashed asymptote y = -1. The branch on the left of x = 2 lies above y = -1 and cuts the y-axis at (0; 1); the branch on the right lies below y = -1. Both branches rise from left to right. The line g(x) = x − 3 passes through the point where the asymptotes cross.

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