IB Maths AA HL 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

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Question 1

Paper 1, no calculatorMedium7 marks

Let $f(x)=x^2-4x+3$ The graph $y=f(x)$ is stretched horizontally by scale factor $2$ Let the resulting graph be $y=F(x)$

(a)

Write down $F(x)$

[2]

(b)

The graph $y=F(x)$ is reflected in the $x$ -axis and then translated upwards by $3$ units, giving $y=g(x)$ Determine $g(x)$ in completed-square form and state the coordinates of its turning point.

[3]

(c)

Instead, starting from $y=F(x)$ translate it upwards by $3$ units and then reflect it in the $x$ -axis, giving $y=h(x)$ Hence, or otherwise, determine whether $h$ has any $x$ -intercepts. Give a reason.

[2]

Question 2

Paper 2, calculatorMedium7 marks

Figure 1 shows the graph of $y=f(x)$ for $-4\leq x\leq 4$

The graph of $y=g(x)$ is obtained from the graph of $y=f(x)$ by reflecting it in the $x$ -axis, applying a vertical stretch with scale factor $2$ and then translating it $1$ unit upwards.

(a)

Write down $f(-2)$

[1]

(b)

On the same axes as Figure 1, sketch the graph of $y=g(x)$ Mark the image of the point on $y=f(x)$ for which $x=-2$

[2]

(c)

Using Figure 1, determine all values of $x$ for which $g(x)=3$

[2]

(d)

For the point $(-2,2)$ on $y=f(x)$ determine its image ordinate if the translation upwards by $1$ unit is performed after the reflection but before the vertical stretch. Hence state whether this order of transformations gives the same graph as $y=g(x)$

[2]

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