Concept explainers
a.
To Determine: The interval in which the function is increasing or decreasing.
The function is increasing on the interval of (−∞,∞) .
Given information:
q(x)=ex+2
Graph:
From the graph, it can be seen that the function is increasing throughout its entire domain, which is (−∞,∞) .
b.
To Determine: The function is odd, even or neither.
The function is neither even nor odd.
Given information:
q(x)=ex+2
Calculation:
A function is even if f(−x)=f(x)
Check if f(−x)=f(x) :
e−x+2≠ex+2
Since e−x+2≠ex+2 , the function is not even.
A function is odd if f(−x)=−f(x)
Multiply −1 by ex+2 :
−f(x)=−(ex+2)
Since −(ex+2)≠ex+2−ex−2≠ex+2 , the function is not odd.
So, the function is neither even nor odd.
c.
To Determine: The extrema of the function, if any.
There are no extrema points.
Given information:
q(x)=ex+2
Calculation:
Find the first derivative of the function.
ex
Differentiate using the Exponential Rule which states that ddx[ax] is axln(a) where a=e .
f′′(x)=ex
To find the local maximum and minimum values of the function, set the derivative equal to 0 and solve:
ex=0
Since there is no value of x that makes the first derivative equal to 0 , there are no local extrema.
Thus, there is no extrema for the function q(x)=ex+2 .
d.
To Determine: The graph of the function related to a graph of one of the twelve basic functions.
The graph is related to exponential function.
Given information:
q(x)=ex+2
Calculation:
From the above graph, it can be seen that the function q(x)=ex+2 is a exponential function since, it shifted 2 units up.
Chapter 1 Solutions
PRECALCULUS:...COMMON CORE ED.-W/ACCESS
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