tmua 2018 Q10

tmua · Uk · paper2 1 marks Function Transformations

The function $\mathrm { f } ( x )$ is defined for all real numbers.
Consider the following three conditions, where $a$ is a real constant:
I $\quad \mathrm { f } ( a - x ) = \mathrm { f } ( a + x )$ for all real $x$.
II $\quad \mathrm { f } ( 2 a - x ) = \mathrm { f } ( x )$ for all real $x$.
III $\mathrm { f } ( a - x ) = \mathrm { f } ( x )$ for all real $x$.
Which of these conditions is/are necessary and sufficient for the graph of $y = \mathrm { f } ( x )$ to have reflection symmetry in the line $x = a$ ?

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The function $\mathrm { f } ( x )$ is defined for all real numbers.

Consider the following three conditions, where $a$ is a real constant:

I $\quad \mathrm { f } ( a - x ) = \mathrm { f } ( a + x )$ for all real $x$.

II $\quad \mathrm { f } ( 2 a - x ) = \mathrm { f } ( x )$ for all real $x$.

III $\mathrm { f } ( a - x ) = \mathrm { f } ( x )$ for all real $x$.

Which of these conditions is/are necessary and sufficient for the graph of $y = \mathrm { f } ( x )$ to have reflection symmetry in the line $x = a$ ?

Paper Questions

Q1 Q2 Q3 Q4 Q5 Q6 Q7 Q8 Q9 Q10 Q11 Q12 Q13 Q14 Q15 Q16 Q17 Q18 Q19 Q20