1 of 8 0-day streak

Analyse reciprocal and square-reciprocal functions

Question 1 of 8

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Consider the function \(f(x)=\frac{-1}{\left(x\right)^2}+1\) for real x in its maximal domain

The reciprocal power is \((x-h)^{-2}\), so use exact values for all marked features

(a)4 marks

Complete the exact feature table for the function

\(x\) \(y\) \(x_{1}\) \(x_{2}\)

(b)1 mark

Choose the domain, range and branch description supported by the exact rule

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

Both branches lie on the same side of the horizontal asymptote, above it

D=\mathbb{R},\qquad R=\left(-\infty,1\right]

Both branches lie on the same side of the horizontal asymptote, below it

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

Both branches lie on the same side of the horizontal asymptote, below it

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

Both branches lie on the same side of the horizontal asymptote, below it

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

Both branches lie on the same side of the horizontal asymptote, below it

Both branches lie on the same side of the horizontal asymptote, above it

(d)2 marks

Evaluate the function at the two exact probe inputs shown below

Input	Output
\(x_1=-3\)	\(f(x_1)=?\)
\(x_2=-2\)	\(f(x_2)=?\)

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