Question

The functions below represent the amounts of water released from two reservoirs over x weeks:

Answer 1

Answer:

• h(x) = -2x^2 -x +3
• Reservoir A releases the same amount of water as Reservoir B over 1 week

Step-by-step explanation:

Given:

  f(x) = x^2 -7x +5

  g(x) = 3x^2 -6x +2

  h(x) = f(x) -g(x)

Find:

  h(x)

  h(1)

Solution:

The expression for h(x) is found by evaluating its definition:

  h(x) = (x^2 -7x +5) -(3x^2 -6x +2)

  h(x) = x^2(1 -3) +x(-7 -(-6)) +(5 -2)

  h(x) = -2x^2 -x +3

Then h(1) is found by substituting 1 for x:

  h(1) = -2(1^2) -(1) +3 = -2 -1 +3

  h(1) = 0 . . . . difference in release amounts after 1 week is 0

The true statements are ...

• h(x) = -2x^2 -x +3
• Reservoir A releases the same amount of water as Reservoir B over 1 week