Answer:
The new function g(x) is steeper than f(x) and shifted to the left 13 units.
Explanation:
Given
[tex]g(x) = 12f(x - 13)[/tex]
Required
Determine the relationship between f(x) and g(x)
First, we need to determine the direction which f(x) is shifted to (right or left)
For a function f(x)
f(x - h) implies that f(x) is shifted right by h units
So, f(x - 13) implies that f(x) is shifted right by 13 units
Next, we determine the steepness of f(x) and g(x)
We can assume that the steepness of f(x) is 1
The steepness of g(x) can be determined as follows:
[tex]g(x) = 12f(x - 13)[/tex]
[tex]g(x) = 12 * f(x - 13)[/tex]
Hence, the steepness of g(x) is 12
Going by the analysis above:
g(x) is steeper and f(x) is shifted 13 units right to get g(x)
