Given that x is an inetger, state the relation representing each equation by making a table of values.
y=3x+5 and -4<x<4
Thanks William
-7, -4, -1, 2, 5, 8, 11, 14, 17
To find the relation representing the equation y = 3x + 5 for the given condition -4 < x < 4, we can create a table of values.
First, let's substitute different values of x into the equation and calculate the corresponding values of y.
For x = -4:
y = 3(-4) + 5
y = -12 + 5
y = -7
For x = -3:
y = 3(-3) + 5
y = -9 + 5
y = -4
For x = -2:
y = 3(-2) + 5
y = -6 + 5
y = -1
For x = -1:
y = 3(-1) + 5
y = -3 + 5
y = 2
For x = 0:
y = 3(0) + 5
y = 0 + 5
y = 5
For x = 1:
y = 3(1) + 5
y = 3 + 5
y = 8
For x = 2:
y = 3(2) + 5
y = 6 + 5
y = 11
For x = 3:
y = 3(3) + 5
y = 9 + 5
y = 14
Since the given condition is -4 < x < 4, we restrict the values of x to the range of -3, -2, -1, 0, 1, 2, and 3. Therefore, the table of values for the given equation is:
x | y
---------
-3 | -4
-2 | -1
-1 | 2
0 | 5
1 | 8
2 | 11
3 | 14
Therefore, the relation representing the given equation y = 3x + 5 for the given condition -4 < x < 4 can be written as:
{(x, y) | x = -3, -2, -1, 0, 1, 2, 3 and y = -4, -1, 2, 5, 8, 11, 14}