Concept explainers
(a)
Graph each function on the same set of axes.
(a)
Explanation of Solution
Given:
Graph:
(b)
Identify the transformation on the graph of the parent function.Find the values caused each transformation.
(b)
Explanation of Solution
Given:
Calculation:
The parent function is
For
For
For
(c)
Find the functions that appear to be stretched or compressed vertically.
(c)
Answer to Problem 44PPS
f(x) and g(x) appear stretched vertically by a factor of 4 units.
Explanation of Solution
Given:
Calculation:
In both of the functions, since x is multiplied by a factor of 16 , they appear stretched vertically by a factor of
(d)
The two functions that are stretched appear to be stretched by the same magnitude.Explain how it is possible.
(d)
Explanation of Solution
Given:
Calculation: In the function f (x), if you take 4 inside the square root , you will get
Similarly , for g(x) , if you take 16 common , you will get
So, in both of the functions, since x is multiplied by a factor of 16 , they appear stretched vertically by a factor of
(e)
Make a table of the rate of change for all three functions between 8 and 12 as compared to 12 and 16. Explain the generalization about rate of change in square root function that can be made as a result of your findings.
(e)
Answer to Problem 44PPS
the rate of change of the square root
Explanation of Solution
Given:
Calculation:
Rate of change of a function
Function | [8,12] | [12,16] |
So, from the table , we observe that the rate of change of the square root
Chapter 7 Solutions
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