Higher November 2021 Paper 4 Q18

OCRHigherCurrent spec6 marksDrawing & Using GraphsGraphical Transformations

18

(a) For each graph below, select its possible equation from this list.
\(y = x\)\(y = x^2\)\(y = \dfrac{1}{x}\)
\(y = \sin x\)\(y = \cos x\)\(y = \tan x\)
\(y = 3^x\)\(y = \left(\dfrac{1}{3}\right)^x\)
(i)
Graph through the origin O that increases to a vertical asymptote, then repeats: branches rising from minus infinity to plus infinity crossing the x-axis, a tan-shaped curve
[1]
(ii)
Increasing curve above the x-axis that approaches the x-axis to the left and crosses the positive y-axis, an exponential growth shape
[1]
(b) Here is a sketch of \(y = x^3\).
Sketch of y = x cubed passing through the origin O

On the axes below, sketch the graphs of

(i) \(y = -x^3\)
Blank x and y axes with origin O

[1]

(ii) \(y = x^3 - 8\), showing the values of any intercepts with the axes.
Blank x and y axes with origin O

[3]

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