IB Maths AA SL AA 2.3 Rational, exponential and logarithmic functions 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.

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Question 1

Paper 1, no calculatorMedium5 marks

The graph of the function rr is shown in Figure 1. It is known that

r(x)=ax+bx+d,x≠−d,r(x)=\frac{ax+b}{x+d}, \qquad x\ne-d,

where a,b,d∈Ra,b,d\in\mathbb R

-4-3-2-1012344321-1-2-3-4(1,1)x=0y=0xy
(a)

Determine the values of aa bb and dd

[3]
(b)

Hence, show that rr is self-inverse, stating the domain of r−1r^{-1}

[2]

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