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

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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]

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