Question

the total reimbursement (in dollars) for driving a company car m miles can be modeled by the function f(x) = 0.45m +5. After a policy change, five more dollars are added on and then the total reimbursement amount is multiplied by 1.25 describe how to transform the graph of f. what is the total reimbursement for a trip of 95 miles?

Answer 1

The slope becomes 0.5625 and y intercept becomes 12.5.

$65.9375

Explanation:

Given that

the total reimbursement function in terms of
`m` miles:

`f(x) = 0.45m +5`

After the policy change, 5 more dollars are added and then total amount is multiplied by 1.25.

To find:

How to transform the graph of f.

Total reimbursement for a trip of 95 miles?

Solution:

`f(x) = 0.45m +5` can also be written as:

`y = 0.45m +5`

It is nothing but slope intercept form, comparing with
`Y = M X+ C`

M is the slope and C is the y intercept.

Slope of the graph is 0.45.

Y intercept is 5.

After change in the function, first of all add $5.

`0.45m + 5+5 = 0.45m+10`

Now, multiply with 1.25

Resulting function becomes:

`f(x) =1.25* (0.45m+10)\\\Rightarrow f(x) =0.5625m+12.5`

Kindly refer to the attached image for the graph of the two functions.

Now, the slope becomes 0.5625 and y intercept becomes 12.5. This is the transformation.

To find the reimbursement for a trip of 95 miles:

Put m = 95

`f(95) =0.5625* 95+12.5 = \bold{\$65.9375 }`