Use input-output tables to determine which graph accurately represents the function f(x)=12x+3 with inputs of −4, −2, 0, 2, and 4.(1 point)
Responses
Five points are plotted on a coordinate plane, and a line is graphed passing through them. The x-axis ranges from 0 to 7 in increments of 1. The y-axis ranges from negative 5 to 5 in increments of 1.
Image with alt text: Five points are plotted on a coordinate plane, and a line is graphed passing through them. The x-axis ranges from 0 to 7 in increments of 1. The y-axis ranges from negative 5 to 5 in increments of 1.
Five points are plotted on a coordinate plane, and a line is graphed passing through them. The x-axis ranges from negative 4 to 4 in increments of 1. The y-axis ranges from negative 10 to 10 in increments of 1.
Image with alt text: Five points are plotted on a coordinate plane, and a line is graphed passing through them. The x-axis ranges from negative 4 to 4 in increments of 1. The y-axis ranges from negative 10 to 10 in increments of 1.
Five points are plotted on a coordinate plane, and a line is graphed passing through them. The x-axis ranges from negative 4 to 4 in increments of 1. The y-axis ranges from negative 10 to 10 in increments of 1.
Image with alt text: Five points are plotted on a coordinate plane, and a line is graphed passing through them. The x-axis ranges from negative 4 to 4 in increments of 1. The y-axis ranges from negative 10 to 10 in increments of 1.
Five points are plotted on a coordinate plane, and a line is graphed passing through them. The x-axis ranges from negative 4 to 4 in increments of 1. The y-axis ranges from negative 10 to 10 in increments of 1.
Image with alt text: Five points are plotted on a coordinate plane, and a line is graphed passing through them. The x-axis ranges from negative 4 to 4 in increments of 1. The y-axis ranges from negative 10 to 10 in increments of 1.
To determine which graph accurately represents the function f(x) = 12x + 3 with inputs of -4, -2, 0, 2, and 4, you can use input-output tables to evaluate the function for each input.
First, let's create an input-output table for the given function:
Input (x) | Output (f(x))
------------------------
-4 | -45
-2 | -21
0 | 3
2 | 27
4 | 51
Now, let's examine each graph and see which one matches the values in the table.
Graph 1: The first graph's description does not provide the coordinates of the plotted points. Therefore, we cannot determine if it accurately represents the function.
Graph 2: The second graph shows the x-axis ranging from -4 to 4 in increments of 1 and the y-axis ranging from -10 to 10 in increments of 1. However, based on the table, the y-values do not match the points on the graph. Hence, this graph does not accurately represent the function.
Graph 3: The third graph's description is exactly the same as the second graph’s description. As we previously determined, the second graph is inaccurate, so this graph is also incorrect.
Graph 4: The fourth graph shows the x-axis ranging from -4 to 4 in increments of 1 and the y-axis ranging from -10 to 10 in increments of 1. Additionally, the points on the graph align with the values in the table. This indicates that graph 4 accurately represents the function f(x) = 12x + 3 with the given inputs.
Therefore, the correct answer is the fourth graph.