Graphs and transformations: DHS 2024 Promo Q3

Dunman High School2024 PromoPromo P1 Q3●●○ Standard4 marks

What this question tests

Graphs of Functions.

Question

. The graph of $y = \mathrm{f}(x)$ has a maximum turning point at $(2,3)$ and passes through the origin. The lines $x = -1$ and $y = 2$ are asymptotes to the graph, as shown in the diagram below.

$Dunman High School 2024 Promo Q3: question diagram$

State the range of values of $x$ for which the graph of $y = \dfrac{1}{\mathrm{f}(x)}$ is increasing. [1]
Sketch the graph of $y = \mathrm{f}'(x)$ , showing clearly the axial intercepts and the asymptotes.

Show full worked solution▾

(a) For $y=\dfrac1{f(x)}$ to be increasing, $y=f(x)$ will be decreasing.

Range of values: $x\ge2$ .

(b)

$Dunman High School 2024 Promo Q3: solution diagram$

Source marking note: SY - vertical asymptote, origin

Source marking note: Is this ok?

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