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Answer the following two questions

What are the key features of a linear function?
Justify why one relation is a function and why the other is not?
Relation 1
x{1 2 3 4}
y{2 4 6 8}
Relation 2: (1, 3), (4, 2), (7, 1), (4, 5)

1 Answer

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Final answer:

The key features of a linear function are slope, y-intercept, and a straight line graph. Relation 1 is a function because each input corresponds to exactly one output, while Relation 2 is not a function because it has two different outputs for the same input.

Step-by-step explanation:

The key features of a linear function are:

  • Slope (m): The slope represents the rate of change between the independent and dependent variables. It describes how the dependent variable changes for every unit increase in the independent variable.
  • Y-intercept (b): The y-intercept is the value of the dependent variable when the independent variable is zero. It represents the starting point of the function on the y-axis.
  • Straight line graph: A linear function forms a straight line on a graph, where each point on the line satisfies the equation y = mx + b.

Now, let's analyze the two given relations to determine if they represent functions:

  1. Relation 1: x{1 2 3 4} y{2 4 6 8}
  • This relation is a function because each input (x-value) corresponds to exactly one output (y-value). For example, when x = 1, y = 2, and when x = 2, y = 4.
Relation 2: (1, 3), (4, 2), (7, 1), (4, 5)
  • This relation is not a function because for x = 4, there are two different y-values: 2 and 5. In a function, each input should have only one output.

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