A function is strictly increasing if its -value always rises as we increase the -value. No section of the graph is allowed to be flat.
On the other hand, a function is increasing if its -value never falls as we increase the -value.
Watch Out! Increasing functions, like the one below, are allowed to have flat sections.
In which intervals is the function (plotted below) strictly increasing? In which intervals is it increasing?
If we follow the graph from left to right, we can see that:
For the graph rises
For the graph falls
For the graph is flat
For the graph rises
Therefore, we conclude that:
The function is strictly increasing on the intervals where it always rises: and
The function is increasing on the intervals where it never falls: and
On which interval(s) is the function $y=f(x)$, shown above, increasing?
|
a
|
$(0, \infty)$ only |
|
b
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$(-\infty, 0) $ and $(1, \infty)$ |
|
c
|
$(-\infty, 0) $ only |
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d
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$(-\infty, 1)$ only |
|
e
|
$(1, \infty)$ only |
On which interval is the function $y=f(x)$, shown above, strictly increasing?
|
a
|
$(-\infty, -1) $ |
|
b
|
$(1, \infty)$ |
|
c
|
$(-\infty, 1) $ |
|
d
|
$(-1,1)$ |
|
e
|
$(-1, \infty)$ |
A function is strictly decreasing if its -value always falls as we increase the -value. No section of the graph is allowed to be flat.
On the other hand, a function is decreasing if its -value never rises as we increase the -value. Decreasing functions are allowed to have flat sections.
In which intervals is the function (plotted below) strictly decreasing? On which intervals is it decreasing?
If we follow the graph from left to right, we can see that:
For the graph rises
For the graph falls
For the graph rises
For the graph is flat
For the graph falls
Therefore, we can conclude that:
The graph is strictly decreasing on the intervals where it always falls: and
The graph is decreasing on the intervals where it never rises: and
On which interval is the function $y=f(x)$, shown above, decreasing?
|
a
|
$(0,1)$ |
|
b
|
$(-\infty, 0) $ |
|
c
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$(-\infty, 1)$ |
|
d
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$(-\infty, 0) \cup(1, \infty)$ |
|
e
|
$(1, \infty)$ |
On which interval is the function $y=f(x)$, shown above, strictly decreasing?
|
a
|
$(1, \infty)$ |
|
b
|
$(-2,0) $ and $ (2, \infty)$ |
|
c
|
$(2, \infty)$ |
|
d
|
$(0,2) $ and $ (2, \infty)$ |
|
e
|
$(-2,2) $ and $ (2, \infty)$ |