1 of 8 0-day streak

Analyse the general rational-power family

Question 1 of 8

No calculator

The point data use the parent coordinate u=n(x-h), so no decimal approximation is needed

The reduced exponent is \(\frac{7}{3}\)

f(x)=-\left(x+1\right)^{\frac{7}{3}}

For the exact key points, use \(u=n(x-h)=r^3\) with parent offsets \(-1\) and \(2\)

(a)1 mark

Analyse the domain, range and central feature before selecting the graph description

The reduced exponent is 7/3. The maximal domain is \mathbb{R} and the range is \mathbb{R}. The graph has point symmetry about (-1,0); its polynomial-like shape is centred at (-1,0) and it has 1 x-intercept.

The reduced exponent is 7/3. The maximal domain is \left[-1,\infty\right) and the range is \left(-\infty,0\right]. The graph has point symmetry about (-1,0); its polynomial-like shape is centred at (-1,0) and it has 1 x-intercept.

The reduced exponent is 7/3. The maximal domain is \mathbb{R} and the range is \mathbb{R}. The graph has point symmetry about (-1,0); its root-like shape is centred at (-1,0) and it has 1 x-intercept.

The reduced exponent is 7/3. The maximal domain is \mathbb{R} and the range is \mathbb{R}. The graph is symmetric about the vertical line x=-1; its polynomial-like shape is centred at (-1,0) and it has 1 x-intercept.

(b)4 marks

Complete the exact feature table. Use the centred ordinate g(u)=f(h+u/n)-k, so the symmetry multiplier satisfies g(-u)=s g(u)

\(y\)-coordinate of key point \(P\) endpoint or centre \(y\)-coordinate \(x\)-coordinate of key point \(P\) endpoint or centre \(x\)-coordinate