IB Maths AA SL AA 2.4 practice question

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]

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