Holt Mcdougal Larson Algebra 2: Student Edition 2012
1st Edition
ISBN: 9780547647159
Author: HOLT MCDOUGAL
Publisher: HOLT MCDOUGAL
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Expert Solution & Answer
Chapter 4.3, Problem 49E
Solution
To graph: The given function and determine the domain and range.
Domain =(−∞,∞)
Range: y>1
Given:
A function g(x)=y=43ex−1+1 is given.
Concept used:
- A exponential function having form y=aerx is said to growth function if a>0 and r>0 and it is said to be decay function if a>0 and r<0 .
- The domain is a set of all real numbers for any natural base functions.
- The range is the set of real numbers above or below the horizontal asymptote y=h . It means if a>0 then f(x)>h and if a<0 then f(x)<h .
Calculation:
The comparison of function y=43ex−1 with y=aerx gives a=43 and r=1 so the function is exponential growth function because a>0 and r>0 .
Evaluate the function at different values of x .
When x=0 the value of y is
y=43e0−1+1y=0.490+1y=1.49
When x=1 the value of y is
y=43e1−1+1y=43+1y=2.33
To sketch the graph, plot the points (0,1.49) and (1,2.33) and draw the curve.
The domain of the function is set of all real numbers. So,
Domain =(−∞,∞)
It is clear from the graph that the horizontal asymptote is y=1 . So, the range is,
y>1
Conclusion:
The domain and range of function is (−∞,∞) and y>1 respectively.
Chapter 4 Solutions
Holt Mcdougal Larson Algebra 2: Student Edition 2012
Ch. 4.1 - Prob. 1GPCh. 4.1 - Prob. 2GPCh. 4.1 - Prob. 3GPCh. 4.1 - Prob. 4GPCh. 4.1 - Prob. 5GPCh. 4.1 - Prob. 6GPCh. 4.1 - Prob. 1ECh. 4.1 - Prob. 2ECh. 4.1 - Prob. 3ECh. 4.1 - Prob. 4E
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Author:Gilbert Strang
Publisher:Wellesley-Cambridge Press
College Algebra (Collegiate Math)
Algebra
ISBN:9780077836344
Author:Julie Miller, Donna Gerken
Publisher:McGraw-Hill Education