1 of 8 0-day streak

Analyse the general rational-power family

Question 1 of 8

No calculator

All powers use the reduced exponent. The input to the power is the exact radicand shown in the rule

The reduced exponent is \(\frac{3}{2}\)

f(x)=\left(x+1\right)^{\frac{3}{2}}-1

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

(a)1 mark

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

The reduced exponent is 3/2. The maximal domain is \left[-1,\infty\right) and the range is \left[-1,\infty\right). The graph has no reflection symmetry about its endpoint or centre; its root-like shape is centred at (-1,-1) and it has 1 x-intercept.

The reduced exponent is 3/2. The maximal domain is \left[-1,\infty\right) and the range is \left[-1,\infty\right). The graph is symmetric about the vertical line x=-1; its polynomial-like shape is centred at (-1,-1) and it has 1 x-intercept.

The reduced exponent is 3/2. The maximal domain is \mathbb{R} and the range is \left[-1,\infty\right). The graph has no reflection symmetry about its endpoint or centre; its polynomial-like shape is centred at (-1,-1) and it has 1 x-intercept.

The reduced exponent is 3/2. The maximal domain is \left[-1,\infty\right) and the range is \left[-1,\infty\right). The graph has no reflection symmetry about its endpoint or centre; its polynomial-like shape is centred at (-1,-1) 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)

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