Question

A coal car on a train weighs 30 tons plus 1 ton per cubic yard of coal x that it carries. The total weight of a coal car is: f(x) = x + 30. How will the graph of this function change if the coal car weight is changed to 26 tons?

The line will shift vertically up by 4 tons.
The line will shift vertically up 26 tons.
The line will shift vertically down by 4 tons.
The line will shift vertically down by 26 tons.

There is no graph.

Answer 1

Think about the original equation and what it represents.

A coal car on a train weighs 30 tons plus 1 ton per cubic yard of coal x that it carries. The total weight of a coal car is: f(x) = x + 30.

"1 ton per cubic yard of coal x" ---> 1*x, or x, cubic tons

"30 tons plus 1 ton per cubic yard of coal x" so the 30 in the original equation represents the weight of the train itself, without the coal.

Now, as the problem says, let's change the weight from 30 to 26. Now the equation becomes

g(x) = x + 26
(I used g(x) instead of f(x) because this is a brand new function)

now, going from f(x) = x + 30 to g(x) = x + 26, what happens to the graph? major hint: we subtracted 4 from the equation f(x) to get g(x).