IB Maths AA SL AA 2.4 Transformations of graphs questions

Exam-style questions in the shape of Paper 1 and Paper 2, with full markschemes. Read the markscheme, or type, photograph or draw your answer and get it marked.

Paper

Paper 1, no calculator Paper 2, calculator

Difficulty

Easy Medium Hard

Question 1

Paper 1, no calculatorEasy6 marks

The function $f$ is defined by $f(x)=x^2$

(a)

The graph $y=u(x)$ is obtained by translating the graph of $y=f(x)$ one unit upwards. Write down $u(x)$

[1]

(b)

The graph $y=v(x)$ is obtained by applying a vertical stretch of scale factor $2$ to the graph of $y=f(x)$ Write down $v(x)$

[1]

(c)

For parts (i) and (ii), the transformations are a translation one unit upwards and a vertical stretch of scale factor $2$

(i)

The graph $y=w(x)$ is obtained by translating the graph of $y=f(x)$ one unit upwards, then applying the vertical stretch. Determine $w(x)$

[2]

(ii)

The graph $y=z(x)$ is obtained by applying the vertical stretch first, then translating the graph of $y=f(x)$ one unit upwards. Write down $z(x)$ and state whether the graphs $y=w(x)$ and $y=z(x)$ are identical, giving a reason.

[2]

Question 2

Paper 1, no calculatorEasy4 marks

The graph of $y=f(x)$ is transformed to the graph of $y=g(x)$ where

f(x)=x^2,\qquad g(x)=-2f(x-1)+3.

(a)

State the horizontal translation used.

[1]

(b)

State the vertical stretch and reflection used to obtain $y=-2f(x-1)$ from $y=f(x-1)$

[2]

(c)

State the final vertical translation.

[1]

Question 3

Paper 1, no calculatorEasy6 marks

The graph of $f$ is shown in Figure 1. The function $g$ is defined by

g(x)=3f(x)+2.

(a)

Use Figure 1 to write down $f(1)$

[1]

(b)

State the transformations that map the graph of $f$ to the graph of $g$ in the order in which they are applied.

[2]

(c)

Hence, sketch the graph of $g$ on the same axes, marking the images of the point on $f$ for which $x=1$ and the vertex of $f$

[3]

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