. A car rental store rents cars for $20 a day. The function f(x) = 20x represents the daily rental fee for x days. The company decides to add a one-time $10 fee for cleaning. Write the function g(x), which gives
the new cost per day, as a transformation of f(x). How would the graph of g(x) compare to that of f(x)?

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.

Step-by-step 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.

answer: the equation matches the regression

step-by-step explanation: