To determine which equation describes the function shown in the mapping diagram with the values given, we first need to analyze the pairs of values provided:
- For \( x = -8 \), \( y = 1 \)
- For \( x = -7.5 \), \( y = 1 \)
- For \( x = -7 \), \( y = 2 \)
- For \( x = -6.5 \), \( y = 3 \)
From these pairs, we notice that as \( x \) increases, \( y \) also increases, implying a linear relationship.
To find the appropriate linear function, we can look for a pattern in the relationship between \( x \) and \( y \).
If we observe the values:
- When \( x = -8 \), \( y \) (unknown value to solve).
- When \( x = -7.5 \), a nod that it can represent an added continuous change in \( y \).
- As this trend continues, we can set up a fitting expression.
Considering the values provided initially, they can be plotted to determine a slope. Assuming \( f(y) = mx + b\), we could infer the transformations as \( y\) represents a function of \( x \).
However, to simplify and derive \( y \) as a function \( f(x) \):
- To extract the coefficients accurately matching the arrows in the diagram, we can select the transformations required to represent \( y \) as directly dependent based on \( x \).
By carefully analyzing possible answers provided: We simplify and fit \( y = \text{(constant) } 12x – 8 \) would fit above observations.
Since the values align based on translation but also adjust in a linear form, the most fitting option is:
- \( f(y) = 12x - 8 \) or \( f(x) = \frac{1}{2}x - 8 \).
Recognizing the arrows convert \( y \) based on projections of \( x\), the relationships would map properly allowing for integer transformations.
Thus, the correct equation that encapsulates the mapping shown in the diagram is:
f(y) = 12x - 8.
1 answer