Math / Algebra

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Use graphs to find the set. $(-1,4) \cap[0,5]$
Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. The set is $\square$ . (Type your answer in interval notation.) B. The set is the empty set.

Studdy Solution

STEP 1

What is this asking? Find where the two intervals overlap on a number line! Watch out! Don't confuse open and closed intervals; they affect where the overlap starts and ends!

STEP 2

1. Draw the intervals
2. Identify the overlap
3. Write the solution in interval notation

STEP 3

Let's start by visualizing these intervals on a number line.
We have two intervals: $(-1, 4)$ and $[0, 5]$ .
- The interval $(-1, 4)$ is an open interval, meaning it includes numbers greater than $-1$ and less than $4$ , but not $-1$ or $4$ themselves. - The interval $[0, 5]$ is a closed interval, meaning it includes numbers from $0$ to $5$ , including $0$ and $5$ .

STEP 4

On a number line, $(-1, 4)$ would look like this: $\text{(---1---0---1---2---3---4---)}$
And $[0, 5]$ would look like this: $\text{[---0---1---2---3---4---5---]}$

STEP 5

Now, let's find where these two intervals overlap.
We're looking for numbers that are in both intervals at the same time!

STEP 6

The overlap starts at $0$ because that's where the closed interval $[0, 5]$ begins, and it ends at $4$ because that's where the open interval $(-1, 4)$ ends.

STEP 7

Since $0$ is included in the overlap (thanks to the closed interval), and $4$ is not included (because of the open interval), the overlap is written as $[0, 4)$ .

STEP 8

The set is $[0, 4)$ .

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QuestionPoints: 0 of 1 Save
Use graphs to find the set. $(-1,4) \cap[0,5]$
Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. The set is $\square$ . (Type your answer in interval notation.) B. The set is the empty set.

Studdy Solution

STEP 1

What is this asking? Find where the two intervals overlap on a number line! Watch out! Don't confuse open and closed intervals; they affect where the overlap starts and ends!

STEP 2

1. Draw the intervals
2. Identify the overlap
3. Write the solution in interval notation

STEP 3

STEP 4

On a number line, $(-1, 4)$ would look like this: $\text{(---1---0---1---2---3---4---)}$
And $[0, 5]$ would look like this: $\text{[---0---1---2---3---4---5---]}$

STEP 5

Now, let's find where these two intervals overlap.
We're looking for numbers that are in both intervals at the same time!

STEP 6

The overlap starts at $0$ because that's where the closed interval $[0, 5]$ begins, and it ends at $4$ because that's where the open interval $(-1, 4)$ ends.

STEP 7

Since $0$ is included in the overlap (thanks to the closed interval), and $4$ is not included (because of the open interval), the overlap is written as $[0, 4)$ .

STEP 8

The set is $[0, 4)$ .

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Studdy Solution

STEP 1

What is this asking? Find where the two intervals overlap on a number line! Watch out! Don't confuse open and closed intervals; they affect where the overlap starts and ends!

STEP 2

1. Draw the intervals2. Identify the overlap3. Write the solution in interval notation

STEP 3

STEP 4

On a number line, (−1,4)(-1, 4)(−1,4) would look like this: (—1—0—1—2—3—4—) \text{(---1---0---1---2---3---4---)} (—1—0—1—2—3—4—)And [0,5][0, 5][0,5] would look like this: [—0—1—2—3—4—5—] \text{[---0---1---2---3---4---5---]} [—0—1—2—3—4—5—]

STEP 5

Now, let's find where these two intervals overlap.We're looking for numbers that are in both intervals at the same time!

STEP 6

The overlap starts at 000 because that's where the closed interval [0,5][0, 5][0,5] begins, and it ends at 444 because that's where the open interval (−1,4)(-1, 4)(−1,4) ends.

STEP 7

Since 000 is included in the overlap (thanks to the closed interval), and 444 is not included (because of the open interval), the overlap is written as [0,4)[0, 4)[0,4).

STEP 8

The set is [0,4)[0, 4)[0,4).

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1. Draw the intervals
2. Identify the overlap
3. Write the solution in interval notation

On a number line, $(-1, 4)$ would look like this: $\text{(---1---0---1---2---3---4---)}$
And $[0, 5]$ would look like this: $\text{[---0---1---2---3---4---5---]}$

Now, let's find where these two intervals overlap.
We're looking for numbers that are in both intervals at the same time!

The overlap starts at $0$ because that's where the closed interval $[0, 5]$ begins, and it ends at $4$ because that's where the open interval $(-1, 4)$ ends.

Since $0$ is included in the overlap (thanks to the closed interval), and $4$ is not included (because of the open interval), the overlap is written as $[0, 4)$ .

The set is $[0, 4)$ .