Considering the doubling plus one function: The output is 2 times the input, plus one. For example, if the input is 3 the out put is 7. Determine which of the following points are on the graph of the doubling plust one fuction:
(2,5), (2,8), (-1,1), (3,4), (-2,-3), (1.5,4), (0.5,1.5)
To determine which points are on the graph of the doubling plus one function, we can plug in the x-coordinate of each point into the function and see if it matches the y-coordinate.
The doubling plus one function is defined as: f(x) = 2x + 1
Let's test each point:
(2,5):
2(2) + 1 = 4 + 1 = 5
The y-coordinate matches, so (2,5) is on the graph.
(2,8):
2(2) + 1 = 4 + 1 = 5
The y-coordinate does not match, so (2,8) is not on the graph.
(-1,1):
2(-1) + 1 = -2 + 1 = -1
The y-coordinate matches, so (-1,1) is on the graph.
(3,4):
2(3) + 1 = 6 + 1 = 7
The y-coordinate does not match, so (3,4) is not on the graph.
(-2,-3):
2(-2) + 1 = -4 + 1 = -3
The y-coordinate matches, so (-2,-3) is on the graph.
(1.5,4):
2(1.5) + 1 = 3 + 1 = 4
The y-coordinate matches, so (1.5,4) is on the graph.
(0.5,1.5):
2(0.5) + 1 = 1 + 1 = 2
The y-coordinate does not match, so (0.5,1.5) is not on the graph.
Therefore, the points (2,5), (-1,1), (-2,-3), and (1.5,4) are on the graph of the doubling plus one function.
To determine which points are on the graph of the doubling plus one function, we need to apply the function to each point and check if the output matches the given coordinates.
The doubling plus one function can be written as f(x) = 2x + 1, where f(x) represents the output.
Let's go through each point one by one:
1. (2, 5):
To check if this point is on the graph, we substitute x = 2 into the doubling plus one function:
f(2) = 2(2) + 1 = 4 + 1 = 5
The output matches the y-coordinate, so this point is on the graph.
2. (2, 8):
To check if this point is on the graph, we substitute x = 2 into the doubling plus one function:
f(2) = 2(2) + 1 = 4 + 1 = 5
The output does not match the y-coordinate, so this point is not on the graph.
3. (-1, 1):
To check if this point is on the graph, we substitute x = -1 into the doubling plus one function:
f(-1) = 2(-1) + 1 = -2 + 1 = -1
The output matches the y-coordinate, so this point is on the graph.
4. (3, 4):
To check if this point is on the graph, we substitute x = 3 into the doubling plus one function:
f(3) = 2(3) + 1 = 6 + 1 = 7
The output does not match the y-coordinate, so this point is not on the graph.
5. (-2, -3):
To check if this point is on the graph, we substitute x = -2 into the doubling plus one function:
f(-2) = 2(-2) + 1 = -4 + 1 = -3
The output matches the y-coordinate, so this point is on the graph.
6. (1.5, 4):
Since the doubling plus one function is defined for integer values of x, we cannot directly substitute x = 1.5 into the function. Therefore, this point is not on the graph.
7. (0.5, 1.5):
Since the doubling plus one function is defined for integer values of x, we cannot directly substitute x = 0.5 into the function. Therefore, this point is not on the graph.
So, the points that are on the graph of the doubling plus one function are:
(2, 5), (-1, 1), and (-2, -3).