If $f(x)=5x+40$, what is $f(x)$ when $x=-5$?
We are given a linear function defined as \(f(x) = 5x + 40\). Our goal is to evaluate this function at the specific point \(x = -5\). This means we need to find the value of \(f(-5)\) by substituting \(-5\) for every occurrence of \(x\) in the function's definition.
To evaluate the function at \(x = -5\), we substitute \(-5\) into the equation:
\[f(-5) = 5(-5) + 40\]
First, perform the multiplication:
\[5 \times (-5) = -25\]
Next, substitute this result back into the equation:
\[f(-5) = -25 + 40\]
Finally, complete the addition:
\[f(-5) = 15\]
After substituting \(x = -5\) into the function \(f(x) = 5x + 40\) and simplifying the expression, we found that \(f(-5) = 15\). Comparing this result with the given choices, we confirm that 15 is the correct value. Therefore, the final answer is \(\boxed{15}\).
Linear functions are widely used in everyday situations to model predictable growth or decline. For instance, if a car rental company charges a base fee of \(\$40\) and an additional \(\$5\) for every mile driven, the total cost \(f(x)\) for driving \(x\) miles would be \(f(x) = 5x + 40\). If you were to drive -5 miles (perhaps in a scenario representing a refund or correcting an error where you returned the car 5 miles early), you could use this formula to calculate the adjustment to the cost, which results in a reduction of \(\$15\) from the baseline or specific context.