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The graph of f(x) is shown below. Estimate and list the value of x where f(x) has a horizontal tangent.
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Answer:
Part A: What is the rate of change and initial value of the function represented by the graph, and what do they represent in this scenario?
First, calculate the rate of change (Slope, once it is a linear function):
I will take the points: and
Let's understand the graph!
This linear graph is about songs being downloaded in a period of 5 weeks.
In the beginning, we have 100 songs to be downloaded. As the weeks past, the number of songs remaining decreases, that's why the graph's slope is negative. In week 5, all songs were downloaded.
The initial value (100) represents the number of songs.
Part B: Write an equation in slope-intercept form to model the relationship between x and y.
The Slope-intercept form of linear equations is
where, m is the slope and b is the y-intercept.
In this case, we have