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? (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.

Answer 1

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

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.

Answer 2

Answer: Then the graph of the function f(x) will change shifting vertically down (because the negative sign in 4) by 4 tons.

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

Solution:

Total weight of a coal car: f(x)=x+30

How will the graph of this function change if the coal car weight is changed to 26 tons?

The total weight of the coal car would be: g(x)=x+26

f(x)=x+30

30=26+4

f(x)=x+26+4

g(x)=x+26

f(x)=g(x)+4

Subtracting 4 both sides of the equation:

f(x)-4=g(x)+4-4

f(x)-4=g(x)

g(x)=f(x)-4

Then the graph of the function f(x) will change shifting vertically down (because the negative sign in 4) by 4 tons.