Question 1 :
[4.5] = ?
Question 2 :
[5.6] = ?
Question 3 :
[-2.3] = ?
Question 4 :
[-5.6] = ?
Question 5 :
[-7.8] = ?
Question 6 :
Graph :
y = [x - 2]
Question 7 :
Graph :
y = [x] + 3
Question 8 :
Graph :
y = [x + 1] + 2
1. Answer :
To have value of [4.5], we have to mark 4.5 on the number line as shown below.
Pick the nearest integer on the left side of 4.5.
That is 4.
[4.5] = 4
2. Answer :
To have value of [5.6], we have to mark 5.6 on the number line as shown below.
Pick the nearest integer on the left side of 5.6.
That is 5.
[5.6] = 5
3. Answer :
To have value of [-2.3], we have to mark -2.3 on the number line as show below below.
Pick the nearest integer on the left side of -2.3.
That is -3.
[-2.3] = -3
4. Answer :
To have value of [-5.6], we have to mark -5.6 on the number line as shown below.
Pick the nearest integer on the left side of -5.6.
That is -6.
[-5.6] = -6
5. Answer :
To have value of [-7.8], we have to mark -7.8 on the number line as shown below.
Pick the nearest integer on the left side of -7.8.
That is -8.
[-7.8] = -8
6. Answer :
y = [x - 2]
The given function is in the form of y - a = [x - b].
Let y = 0 and x - 2 = 0. Then, y = 0 and x = 2.
From y = 0, there is no vertical shift.
From x = 2, we have an horizontal shift of 2 units to the right.
So each point of the parent function to be shifted 2 units to the right.
If we do the above transformation, we will have a graph as given below.
7. Answer :
y = [x] + 3
If we write the given function in the form of
y - a = [x - b],
we will have y - 3 = [x].
Let y - 3 = 0 and x = 0. Then, y = 3 and x = 2.
From y = 3, we have a vertical shift of 3 units up.
From x = 0, there is no horizontal shift.
So each point of the parent function to be shifted 3 units up.
If we do the above transformation, we will have a graph as given below.
8. Answer :
y = [x + 1] + 2
If we write the given function in the form of
y - a = [x - b],
we will have y - 2 = [x + 1].
Let y - 2 = 0 and x + 1 = 0. Then y = 2 and x = -1.
From y = 2, we have a vertical shift of 2 units up.
From x = - 1, we have an horizontal shift of 1 unit to the left.
So each point of the parent function to be shifted 2 units up and 1 unit to the left.
If we do the above transformations, we will have a graph as given below.
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