Answer:
The function g(x) as a transformation of f(x) is g(x) = f(x) + 10.
The graphs of g(x) and f(x) will be straight line graphs.
The graph of g(x) will intercept the y-axis at 10 and the graph of f(x) will intercept the y-axis at 0.
Explanation:
From the question,
The function f(x) = 20x represents the daily rental fee for x days. Then the added a one-time $10 fee for cleaning.
Hence, the daily rental fee for x days will now be 20x + 10.
The new cost per day g(x) as a transformation of f(x) will be
Since the new cost per day is 20x + 10
∴ g(x) = 20x + 10
But f(x) = 20x
Hence,
g(x) = f(x) + 10
For how the graph of g(x) will compare to that of f(x)
The general equation of a straight line is y = mx + c
Where y indicates the y-axis, x indicates the x-axis, m indicates the gradient and c is the intercept on the y-axis.
Hence, both graphs of g(x) and f(x) will be straight line graphs.
For f(x) = 20x
Comparing this function to the general equation of straight line,
The intercept c is 0. Hence, the graph will intercept the y-axis at 0.
For g(x) = f(x) + 10
Then, g(x) = 20x + 10
Comparing this function to the general equation of straight line,
The intercept c is 10. Hence, the graph will intercept the y-axis at 10.