Big Ideas Math Algebra 1, 2015
BI
Big Ideas Math Algebra 1, 2015 View details
7. Piecewise Functions
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Exercise 55 Page 224

Practice makes perfect
a We will graph the function before we write its equation. We assume that there was no snow when the snowstorm started, making the graph start at
Diagram with the starting point of the function
Let's look at the situation sentence by sentence and add pieces to our graph as we go. We are told that the snow fell inch per hour for hours.
Let's graph the first piece of the function, knowing that after hours we have inches of snow.
Diagram with the first piece of the function
Next, we are told that it snowed inches per hour for the following hours. This gives us the second piece of the function, which we need to add to the first piece.
We can add this piece to our graph.
Diagram with the first and the second piece of the function
Lastly, it snowed more inch in the That gives us the third and final piece of the function.
We can add this final piece to the graph.
Diagram with the first, the second and the third piece of the function

For each of these intervals, we can write an equation for the line in slope-intercept form. Let's look at this individually.

First Piece

For the first piece we know that there is inch of snow added every hour. This gives us a slope of It begins at hour so the intercept is at the origin, Let's use this to write the equation.
This describes the snowfall for the first hours. Knowing both the equation and the interval, we can write the first piece of the function.

Second Piece

The second piece represents a snowfall of inches each hour, which means that it has a slope of We also know that it begins at the point Let's use this point to solve for in slope-intercept form.
Solve for
Recall that this interval began at hour and ended at hour

Third Piece

The third piece represents a snowfall of inch per hour, giving it a slope of We can use the starting point of this piece to solve for in slope-intercept form.
Solve for
This rate started in the hour and lasted for hour, until the storm ended. Its domain is then


b Graphically the amount of snow accumulated during the storm is represented as the highest point on the graph.
Diagram with the first, the second and the third piece of the function. The highest point is marked.
At the end of the storm a total of inches of snow had accumulated. Thus, the friend is incorrect.