Question 10 \[ \text { If } f(x)=-2 x+3 \text { then } f(3)-f(4)= \]

To find \( f(3) - f(4) \), we first calculate \( f(3) \) and \( f(4) \) using the given function \( f(x) = -2x + 3 \). Calculating \( f(3) \): \[ f(3) = -2(3) + 3 = -6 + 3 = -3 \] Calculating \( f(4) \): \[ f(4) = -2(4) + 3 = -8 + 3 = -5 \] Now, we find the difference: \[ f(3) - f(4) = -3 - (-5) = -3 + 5 = 2 \] Therefore, \( f(3) - f(4) = 2 \). --- When linear functions like \( f(x) = -2x + 3 \) are involved, it's fascinating to note that they represent straight lines on a graph. Each point on the line corresponds to a different value of \( x \), creating a visual representation of equation behaviors. In real-world scenarios, linear functions often model relationships such as distance over time or budgeting. For example, if this function represented costs, it could show how expenses might decrease as discounts are applied over time. Understanding linear functions can simplify complex problems in everyday situations!