Concept explainers
To Compare: The given graph with parent function
Answer to Problem 9CA
The graph has been vertically translated up for 3 units and vertical shrink for the factor of 0.5.
Explanation of Solution
Given information: We are given with the function
Formula used: The exponential function is given by
Calculation:
Let’s find the function of the given graph using the points on the graph (0, 3.5), (1, 4) and (2, 5)
Let’s use (0, 3.5)
Use (1, 4)
Use (2,5)
Solve the system of equations for a, b and c.
Subtract equations (1)-(2) and (2)-(3)
Factor each,
Divide them,
It gives
Now, plug in back b as 2 into
Now, plug in these values of ‘a’ and ‘b’ into equation (2)
Subtract both sides 1
So, the function for the graph is
Conclusion: So, there is vertical shrink or compression for the factor of 0.5 and vertical translation for 3 units.
Chapter 6 Solutions
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