Concept explainers
The complete analysis of given function.
Domain:
Range:
Continuity:
Increasing-decreasing behaviour: The graph is always increasing.
Symmetry: The function is odd, so, the graph is symmetric about the origin.
Boundedness: Upper and lower bound
Local extrema: No Local Extrema
Horizontal asymptotes: No Asymptotes
Vertical asymptotes: No Asymptotes
End behaviour: Th graph falls to the left and rises to the right
Given:
Graph:
Domain:
The domain of the expression is all real numbers except where the expression is undefined. In this case, there is no real number that makes the expression undefined.
Interval Notation:
Set-Builder Notation:
Range:
The range is the set of all valid
Interval Notation:
Set-Builder Notation:
Continuity:
Since the domain is all real numbers,
Increasing-decreasing behaviour:
The function
Symmetry:
To determine if the function is odd, even, or neither in order to find the symmetry.
If the function is odd, the function is symmetric about the origin. And ff the function is even, the function is symmetric about the y-axis.
Find
A function is even if
Check if
Since
The function is not even.
A function is odd if
Multiply
Since
The function is odd.
Since the function is odd, the graph is symmetric about the origin.
Boundedness:
Find every combination of
If a polynomial function has integer coefficients, then every rational zero will have the form
Find every combination of
Apply synthetic division on
Since
Upper and lower bound:
Local extrema:
Differentiate
Since
To find the local maximum and minimum values of the function, set the derivative equal to
Since there is no value of
Horizontal asymptotes:
Since
Vertical asymptotes:
Since
End behaviour:
The largest exponent is the degree of the polynomial is
Since the degree is odd, the ends of the function will point in the opposite directions. Falls to the left and rises to the right
Since the leading coefficient is positive, the graph rises to the right.
From analysing the graph, the function falls to the left and rises to the right
Chapter 2 Solutions
PRECALCULUS:GRAPHICAL,...-NASTA ED.
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