Easy -1.8 This is a multiple-choice question testing basic understanding of when sign change method fails (discontinuity). Students only need to recognize that f(x)=1/x has a discontinuity at x=0, requiring minimal calculation or conceptual depth—well below average A-level difficulty.
2 A student is searching for a solution to the equation \(\mathrm { f } ( x ) = 0\)
He correctly evaluates
$$f ( - 1 ) = - 1 \text { and } f ( 1 ) = 1$$
and concludes that there must be a root between - 1 and 1 due to the change of sign.
Select the function \(\mathrm { f } ( x )\) for which the conclusion is incorrect.
Circle your answer.
$$\mathrm { f } ( x ) = \frac { 1 } { x } \quad \mathrm { f } ( x ) = x \quad \mathrm { f } ( x ) = x ^ { 3 } \quad \mathrm { f } ( x ) = \frac { 2 x + 1 } { x + 2 }$$
2 A student is searching for a solution to the equation $\mathrm { f } ( x ) = 0$
He correctly evaluates
$$f ( - 1 ) = - 1 \text { and } f ( 1 ) = 1$$
and concludes that there must be a root between - 1 and 1 due to the change of sign.\\
Select the function $\mathrm { f } ( x )$ for which the conclusion is incorrect.\\
Circle your answer.
$$\mathrm { f } ( x ) = \frac { 1 } { x } \quad \mathrm { f } ( x ) = x \quad \mathrm { f } ( x ) = x ^ { 3 } \quad \mathrm { f } ( x ) = \frac { 2 x + 1 } { x + 2 }$$
\hfill \mbox{\textit{AQA Paper 1 2020 Q2 [1]}}