1 of 8 0-day streak

Analyse reciprocal and square-reciprocal functions

Question 1 of 8

Calculator allowed

Consider the function \(f(x)=\frac{-4}{\left(x\right)}-1\) for real x in its maximal domain

The reciprocal power is \((x-h)^{-1}\), so use exact values for all marked features

(a)3 marks

Complete the exact feature table for the function

\(x\) \(y\) \(x_{1}\)

(b)1 mark

Which option records the excluded values and the branch positions correctly?

D=\mathbb{R}\setminus\left\{0\right\},\qquad R=\mathbb{R}\setminus\left\{1\right\}

The branches are above and to the left, and below and to the right, of the asymptote intersection

D=\mathbb{R}\setminus\left\{0\right\},\qquad R=\mathbb{R}\setminus\left\{-1\right\}

The branches are above and to the left, and below and to the right, of the asymptote intersection

D=\mathbb{R}\setminus\left\{0\right\},\qquad R=\mathbb{R}\setminus\left\{-1\right\}

The branches are above and to the right, and below and to the left, of the asymptote intersection

D=\mathbb{R},\qquad R=\mathbb{R}

The branches are above and to the left, and below and to the right, of the asymptote intersection

Select the branch orientation implied by the sign of the normalised coefficient

The branches are above and to the left, and below and to the right, of the asymptote intersection

The branches are above and to the right, and below and to the left, of the asymptote intersection

(d)2 marks

Evaluate the function at the two exact probe inputs shown below

Input	Output
\(x_1=1\)	\(f(x_1)=?\)
\(x_2=-1\)	\(f(x_2)=?\)

\(f(x_{1})\) \(f(x_{2})\)