Concept explainers
In Problem 1-3:
Determine the slope and y-intercept of each linear function.
Graph each function. Label the intercepts.
Determine the domain and the range of each function.
Determine the average rate of change of each function.
Determine whether the function is increasing, decreasing of constant.
(a)
The slope and y-intercept of the linear function
Explanation of Solution
Given information:
The linear function is
Explanation:
Let us consider the function,
Compare the given function
Hence, the slope
(b)
To graph: The function
Explanation of Solution
Given information:
The linear function is
Graph:
Graph the function
Solve the equation
Now, add 5 on both sides below in value.
Divide 2 on both sides below in value.
Therefore, the x-intercept is
Then, the graph of the function
At first mark the x-intercept and y-intercepts on the axes and then join them with a straight edge
as shown in the following diagram.
(c)
The domain and the range of thefunction
Explanation of Solution
Given information:
The given function is
Explanation:
Find the domain and range of the given function
Observe the above diagram, in which the function
The graph a along both sides of the x-axis without gaps, it means the domain of the given function is all real numbers.
Therefore the domain of the function
And also observed that, the graph is along both sides of the y-asix without gaps, it
Since, the range of the function
Hence, the function f is decreasing.
(d)
The average rate of change of the given function
Explanation of Solution
Given information:
The given function is
Explanation:
Calculate the average rate of the functions
The average rate of the function
The average rate of a linear function is its slope: therefore the average rate of the function
(e)
Whether the function is
Explanation of Solution
Given information:
The given function is
Explanation:
Determine whether the function is increasing, decreasing or constant.
Write the fact that, a linear function with positive slope is always an increasing function:
Apply the fact to check the behavior of the graph of the given function.
Therefore the given function
Hence, the function
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