To determine the correct equation describing the function shown in the mapping diagram, we need to analyze the relationship between the values in ovals \( x \) and \( y \) as indicated by the arrows.
Given the choices, it seems we are looking for a function \( f \) that relates values from \( x \) to \( y \).
The format of the equations involves determining how a value \( x \) maps to \( y \), which can generally be described with an equation \( y = f(x) \).
- The first potential function, \( f(x) = 8x - 12 \), indicates that for each \( x \), we multiply by 8 and subtract 12 to get \( y \).
- The second option, \( f(x) = 8x - \frac{1}{2} \), suggests a similar relationship but with a smaller subtraction.
- The third option, \( f(x) = 12x - 8 \), suggests a different multiplication factor (12 instead of 8) with a smaller subtraction.
- The fourth option, \( f(x) = \frac{1}{2} x - 8 \), indicates a completely different relationship, implying the output \( y \) grows much slower than \( x \).
- The last two options \( f(y) \) rewrite the functions in terms of \( y \), which isn't standard for mapping values from \( x \) to \( y \).
Without knowing the exact values in the ovals, the correct equation would depend on the nature of the transformation indicated by the arrows between the two sets.
Based on typical mapping behaviors, if we assume the simplest case where the first choice (or any choice) directly corresponds proportionately, testing the simplest linear option would be best.
If values in \( x \) increase linearly alongside a clear observable trend—for example, if \( y \) was noted consistently as \( 8x - 12 \) through data points (for instance), that would lend credence to \( f(x) = 8x - 12 \) being the correct option.
So, based on the analysis and the common convention in mapping diagrams, I'd conclude that:
The most likely equation for the function is:
\[ f(x) = 8x - 12 \]
Please refer to the specific mapping to verify the precise values for the most accurate conclusion!