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i) The given function is
The domain is
ii) For vertical asymptotes, we simplify the function to get;
The vertical asymptote occurs at
iii) The roots are the x-intercepts of the reduced fraction.
Equate the numerator of the reduced fraction to zero.
iv) To find the y-intercept, we substitute into the reduced fraction.
v) The horizontal asymptote is given by;
The horizontal asymptote is .
vi) The function has a hole at .
Thus at .
This is the factor common to both the numerator and the denominator.
vii) The function is a proper rational function.
Proper rational functions do not have oblique asymptotes.
Answer:
Step-by-step explanation:
We are given that
Function f decreases from quadrant 2 to quadrant 1 and approaches y=0
It cut the y- axis at (0,6) and passing through the point (1,2).
Function g(x) approaches y=0 in quadrant 2 and increases into quadrant 1.
It passing through the point (-1,2) and cut the y-axis at point (0,6).
Reflection across y- axis:
Rule of transformation is given by
Using the rule then we get
By using
Substitute x=-1
Substitute x=0
Therefore, is true.
