Respuesta :
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.
Answer:
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.
