Acoal 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? (1 point) a the line will shift vertically up by 4 tons. b the line will shift vertically up 26 tons. c the line will shift vertically down by 4 tons. d the line will shift vertically down by 26 tons.

Option c. The line will shift vertically down by 4 tons.

Step-by-step explanation:

A coal car on a train weighs 30 tons, plus 1 ton per cubic yard of coal 'x' that the car contains.

The function formed for total weight of a coal car is f(x) = x + 30

If the coal car weight is changed from 30 tons to 26 tons then the new (changed) function will be g(x) = x + 26

Now we have to find the relation between these functions.

f(x) = x + 30 ⇒ f(x) = x + 26 + 4

since g(x) = x + 26 so by replacing value of (x + 26) by g(x)

f(x) = g(x) + 4

Now the relation formed will be g(x) = f(x) - 4

Finally it is clear from the relation [g(x) = f(x) - 4] that graph formed for f(x) will be shifted vertically down by 4 tons to form the new function g(x).

Therefore, option c. The line will shift vertically down by 4 tons is correct.

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step-by-step explanation: