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Worked solution

Translate all seven interval rows

Complete the following table.

RowSet notationInterval notation
1Find the set notation[−3,5)[-3,5)
2{x∈R:1<x≤10}\{x\in\mathbb R:1<x\le10\}Find the interval notation
3{y∈R:y≥−1}\{y\in\mathbb R:y\ge-1\}Find the interval notation
4Find the set notation(−∞,−6)(-\infty,-6)
5{w∈R:w≠2}\{w\in\mathbb R:w\ne2\}Find the interval notation
6{w∈R:−4<w≤−2 or w>5}\{w\in\mathbb R:-4<w\le-2\text{ or }w>5\}Find the interval notation
7R∖{3}\mathbb R\setminus\{3\}Find the interval notation

CJC · Functions · Self-Practice 1

Row 1

Answer

{x∈R:−3≤x<5}\{x\in\mathbb R:-3\le x<5\}.

The square bracket includes −3 and the round bracket excludes 5.

How did this part go?

Row 2

Answer

(1,10](1,10].

The strict lower inequality gives a round bracket; the weak upper inequality gives a square bracket.

How did this part go?

Row 3

Answer

[−1,∞)[-1,\infty).

Include −1; infinity is not a real endpoint and always takes a round bracket.

How did this part go?

Row 4

Answer

{y∈R:y<−6}\{y\in\mathbb R:y<-6\}.

The round bracket excludes −6. The source uses the variable y for this row.

How did this part go?

Row 5

Answer

(−∞,2)∪(2,∞)(-\infty,2)\cup(2,\infty).

Split the real line at the excluded value 2 and leave both copies of that boundary open.

How did this part go?

Row 6

Answer

(−4,−2]∪(5,∞)(-4,-2]\cup(5,\infty).

Translate each piece separately and join them with a union: or means either piece is allowed.

How did this part go?

Row 7

Answer

(−∞,3)∪(3,∞)(-\infty,3)\cup(3,\infty).

Removing the singleton {3} leaves the two open rays on either side.

How did this part go?

Solution notes

All seven answers are printed in both copies; the reasons are independent teaching explanations. Row numbers identify the source table rows; no printed marks are added.