Answer:
First, we need to know when the function is increasing, and when is decreasing.
When a function is increasing, it's because to higher <em>x-values </em>belong higher <em>y-values. </em>On the other hand, a function is decreasing when to higher <em>x-values </em>belong lower <em>y-values. </em>The effect in the graph will be a upwards direction of the function when is increasing, and a downwards direction when is decreasing.
So, according to the given graph, we see that between 0 and 4 is increasing, the higher x-values are, higher y-values are. Between 4 and 6 is decreasing, is downwards. Between 6 and 8 is increasing. Between 8 and 10 is decreasing. In finally, between 10 and 14 is neither decreasing or increasing, it remains horizontal.
All these interpretations we can expressed using math language, specifically inequalities:
- 0 < x < 4: increasing.
- 4 < x < 6: decreasing.
- 6 < x < 8: increasing.
- 8 < x < 10: decreasing.
- 10 < x < 14: neither increasing or decreasing.
i) The given function is
The factored form is
The domain are the values of x for which the function is defined.
ii) To find the vertical asymptotes, equate the denominator to zero.
iii) To find the roots, equate the numerator to zero.
The root is
iv) To find the y-intercept, put into the function.
The y-intercept is
v) The horizontal asymptote is given by;
The horizontal asymptote is
vi) The function is not reducible. There are no holes.
vii) The given function is a proper rational function.
Proper rational functions do not have oblique asymptotes.
Solution
For this case we have this function given:
And we want to find -f(x) so we can do this:
And we can take common factor x and we got:
Answer:
3rd option
Step-by-step explanation:
You first notice that 12 and 75 are multiples of 3. Your expression becomes
. At this point you should recognize it's and . The second term gets factored as a difference of squares:
Answer:
Step-by-step explanation:
x% of 40 = 22
(x/100)×40 = 22
x = 22×100/40 = 55
22 is 55% of 40
:::::
35% of 60 = 0.35×60 = 21