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Analyse sideways-parabola and root-function families

QUESTION TYPEMix of allChange

Question 1 of 8

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Consider the relation \(r\) given by the rule below

\left(y+2\right)^2=-\frac{3}{2}\left(x-\frac{8}{3}\right)

Find the defining point, exact intercepts and the listed probe points

(a)5 marks

Find the defining point, exact intercepts and the listed probe points

vertex \(x\) vertex \(y\) \(x_0\) \(y_{0,1}\) \(y_{0,2}\)

(b)1 mark

Choose the domain and range statement that matches the rule

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

\mathcal{D}=\left(-\infty,\frac{8}{3}\right),\qquad\mathcal{R}=\mathbb{R}

\mathcal{D}=\left(-\infty,\frac{8}{3}\right],\qquad\mathcal{R}=\mathbb{R}

\mathcal{D}=\mathbb{R},\qquad\mathcal{R}=\left(-\infty,\frac{8}{3}\right]

Choose the branch or relation represented by the displayed rule

\left(y+2\right)^2=-\frac{3}{2}\left(x-\frac{8}{3}\right)

y=-2 + \sqrt{-\frac{3}{2}\left(x-\frac{8}{3}\right)}

y=-2 - \sqrt{-\frac{3}{2}\left(x-\frac{8}{3}\right)}

(d)1 mark

Decide whether the displayed relation is a function of \(x\)

Some allowed inputs are paired with two outputs

It is not a function because it is not one-to-one

Each allowed input is paired with exactly one output

(e)3 marks

Enter the exact coordinates of the listed probe points

\(x_1\) \(y_{1,1}\) \(y_{1,2}\)