Analyse semicircles and circular regions practice questions | Mathematical Methods (Year 11, VCE Units 1 & 2)

(a)1 mark

Select the equation for the named semicircle

y=4+\sqrt{37-\left(x+1\right)^2}

y=4+\sqrt{37-\left(x-1\right)^2}

y=4-\sqrt{37-\left(x+1\right)^2}

y=4+\sqrt{\sqrt{37}-\left(x+1\right)^2}

(b)1 mark

Is the selected semicircle relation a function?

The relation is a function

The relation is not a function

(c)1 mark

Select the exact domain and range of the relation in part (a)

D=[-1-\sqrt{37},\;-1+\sqrt{37}],\quad R=[4,\;4+\sqrt{37}]

D=[-1-\sqrt{37},\;-1+\sqrt{37}],\quad R=[4-\sqrt{37},\;4]

D=[4,\;4+\sqrt{37}],\quad R=[-1-\sqrt{37},\;-1+\sqrt{37}]

D=(-1-\sqrt{37},\;-1+\sqrt{37}),\quad R=(4,\;4+\sqrt{37})