5. Intervals of Increase and Decrease
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Analyze the behavior of the output variable] y.
& In interval (a), the function is increasing. & In interval (b), the function is constant. & In interval (c), the function is decreasing. & In interval (d), the function is constant.
We consider a device that monitors the voltage across a lamp over time. The given graph shows the results of the voltage measurements over time.
& In interval (a), the function is increasing. & In interval (b), the function is . & In interval (c), the function is . & In interval (d), the function is . The function is said to be decreasing when as the input variable x increases, the output variable y decreases. Therefore, the given function is decreasing in interval (c). & In interval (a), the function is increasing. & In interval (b), the function is . & In interval (c), the function is decreasing. & In interval (d), the function is . Finally, we can conclude that the function is constant in intervals (b) and (d), since its output values does not change as the input value increases. & In interval (a), the function is increasing. & In interval (b), the function is constant. & In interval (c), the function is decreasing. & In interval (d), the function is constant.