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A linear function is a function that has constant average rate of change;
Also, a relation that represents a function must have unique input and output values.
<h3>Question 11: Relations and Functions</h3>A relation may or may not represent a function.
When the domain and the range of a relation are unique, then the relation is a function.
So, the true option is (b) function
<h3>Question 12: Relations and Functions</h3>A one-to-many relation is not a function.
This is so because the domain and the range of the function are not unique
So, the true option is (c) figure 3: one-to-many.
<h3>Question 13: Variables</h3>A dependent variable is a variable that depends on other variables for its value.
In this case, the dependent variable is (b) boosts the immune system.
<h3>Question 14 and 15: Domain and Range</h3>The domain is the set of input values (i.e. the x values), while the range is the set of output values (i.e. the y values)
This means that:
- The domain of the function is: (a) {2,3,4,5,6}
- The range of the function is: (b) {4,6,8,10,12}
The graph of a linear function is represented by a straight line, and it has a constant slope or rate.
This means that:
- Graph C is a linear function
- Table B is a linear function
The fare of 3 km and 5 km are given as 35 pesos and 55 pesos, respectively.
This means that:
Table (b) represents the information
<h3>Question 19: The linear equation</h3>Start by calculating the slope (m) using:
So, we have:
The linear equation is then calculated as:
This gives
This means that:
The linear equation that describes the relationship is (c) ;
This means that x = 4.
So, we have:
Hence, the fare will be (a) 45 pesos
Read more about linear functions at: