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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)

Analyse the rule by calculating its key point, intercepts and probe coordinates

(a)5 marks

Analyse the rule by calculating its key point, intercepts and probe coordinates

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

(b)1 mark

Which paired statement gives the allowed inputs and outputs?

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

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

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

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

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

Each allowed input is paired with exactly one output

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

(e)3 marks

Enter the exact coordinates of the listed probe points

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