Find the value of $h(-7)$ for the function below.
$h(x)=5.7-19 x$
The objective is to evaluate the linear function \(h(x) = 5.7 - 19x\) at the specific value \(x = -7\). A linear function is a mathematical relationship where the variable \(x\) is raised to the power of one and multiplied by a constant coefficient, with another constant term added. Here, the coefficient is \(-19\) and the constant term is \(5.7\). Evaluating this function involves substituting the input value into the expression and performing the arithmetic operations according to the order of operations.
To find the value of \(h(-7)\), we substitute \(x = -7\) into the given function expression:
\[h(-7) = 5.7 - 19(-7)\]
First, we perform the multiplication \(19 \times (-7)\). Since the product of two negative numbers is positive, we compute the product of their absolute values and consider the negative sign carefully:
\[19 \times (-7) = -133\]
Now, substitute this result back into the expression for \(h(-7)\):
\[h(-7) = 5.7 - (-133)\]
Subtracting a negative number is equivalent to adding its positive counterpart:
\[h(-7) = 5.7 + 133\]
Adding these two numbers together gives:
\[h(-7) = 138.7\]
Comparing our calculated value of \(138.7\) with the provided options:
The value \(138.7\) matches the final option. Thus, the correct value for the function at \(x = -7\) is \(\boxed{138.7}\).
Linear functions are widely used in economics to model costs and revenue. For example, if a business has a fixed daily operating cost and variable costs based on the number of units produced, the total cost can be modeled as a linear function. Similarly, finding the value of a function at a specific point, as we did here, is analogous to calculating the expected outcome for a specific scenario, such as predicting the total production cost for a given number of units, helping businesses make informed financial decisions.