To determine the correct equation that describes the function shown in the mapping diagram, we would usually analyze the relationship between the values in the x oval and the values in the y oval based on the arrows connecting them.
For your question, we need to infer the relationship between x and y based on the options provided.
If we assume that the arrows indicate that each value in x is transformed to a corresponding value in y through a mathematical function, let's consider the form of the equations:
- The options with \( f(x) \) suggest that y is a function of x.
- The options with \( f(y) \) imply that y itself is being used to express x, which is less common in standard function notation but possible.
Given common function forms:
- Linear transformation functions would typically be represented as \( f(x) = mx + b \), where \( m \) is the slope and \( b \) is the y-intercept.
Assuming we want to express y in terms of x, the most common forms would include using x directly in the function.
Looking at the choices:
- \( f(x) = 12x - 8 \)
- \( f(x) = \frac{1}{2}x - 8 \)
- \( f(x) = 8x - \frac{1}{2} \)
- \( f(y) = 8x - \frac{1}{2} \)
Since we are looking for a relationship that directly uses x to determine y, and given the potential functions could fit based on a standard linear relationship, a reasonable assumption would lead us towards the second option:
f(x) = \frac{1}{2}x - 8
Please double-check your particulars about the mapping and scaling from values in x to y based on the diagram for precise determination, but given the nature of the answers, this seems to be a plausible candidate.
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