Search

1 of 8 0-day streak

Analyse sideways-parabola and root-function families

QUESTION TYPEMix of allChange

Question 1 of 8

Calculator allowed

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

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

Record the defining point and all requested exact coordinates for this family

(a)5 marks

Record the defining point and all requested exact coordinates for this family

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

(b)1 mark

Select the exact domain and range of the relation or function

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

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

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

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

Choose the branch or relation represented by the displayed rule

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

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

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

(d)1 mark

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

Each allowed input is paired with exactly one output

Some allowed inputs are paired with two outputs

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

(e)3 marks

Enter the exact coordinates of the listed probe points

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