Exercise 8 Page 193

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.

There are four intervals,

(a),

(b),

(c),

and

(d),

for which we want to describe the behavior of the function. We can say that the function is increasing when as the input variable

x

increases, the output variable

y

also increases. Our function behaves like this in interval

(a) .

In interval (a), the function is increasing . In interval (b), the function is c o n s t a n t . In interval (c), the function is decreasing . In interval (d), the function is c o n s t a n t .

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 c o n s t a n t . In interval (c), the function is decreasing . In interval (d), the function is c o n s t a n t .

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 .