To determine which point lies on the graph of the function [tex]\( y = |8 - 2x| + 3 \)[/tex], let's go through the step-by-step process of evaluating this function at each given [tex]\( x \)[/tex]-value.
### Step-by-Step Evaluation
1. Evaluate the function at [tex]\( x = 6.2 \)[/tex]
- Calculate [tex]\( |8 - 2 \cdot 6.2| + 3 \)[/tex]
- [tex]\( 2 \cdot 6.2 = 12.4 \)[/tex]
- [tex]\( 8 - 12.4 = -4.4 \)[/tex]
- [tex]\( |-4.4| = 4.4 \)[/tex]
- [tex]\( 4.4 + 3 = 7.4 \)[/tex]
So, the point [tex]\((6.2, 7.4)\)[/tex] satisfies the function.
2. Evaluate the function at [tex]\( x = 7.8 \)[/tex]
- Calculate [tex]\( |8 - 2 \cdot 7.8| + 3 \)[/tex]
- [tex]\( 2 \cdot 7.8 = 15.6 \)[/tex]
- [tex]\( 8 - 15.6 = -7.6 \)[/tex]
- [tex]\( |-7.6| = 7.6 \)[/tex]
- [tex]\( 7.6 + 3 = 10.6 \)[/tex]
So, the point [tex]\((7.8, 11.2)\)[/tex] does not satisfy the function.
3. Evaluate the function at [tex]\( x = 8.6 \)[/tex]
- Calculate [tex]\( |8 - 2 \cdot 8.6| + 3 \)[/tex]
- [tex]\( 2 \cdot 8.6 = 17.2 \)[/tex]
- [tex]\( 8 - 17.2 = -9.2 \)[/tex]
- [tex]\( |-9.2| = 9.2 \)[/tex]
- [tex]\( 9.2 + 3 = 12.2 \)[/tex]
So, the point [tex]\((8.6, 6.8)\)[/tex] does not satisfy the function.
4. Evaluate the function at [tex]\( x = 9.6 \)[/tex]
- Calculate [tex]\( |8 - 2 \cdot 9.6| + 3 \)[/tex]
- [tex]\( 2 \cdot 9.6 = 19.2 \)[/tex]
- [tex]\( 8 - 19.2 = -11.2 \)[/tex]
- [tex]\( |-11.2| = 11.2 \)[/tex]
- [tex]\( 11.2 + 3 = 14.2 \)[/tex]
So, the point [tex]\((9.6, 7.3)\)[/tex] does not satisfy the function.
### Conclusion
After evaluating the function [tex]\( y = |8 - 2x| + 3 \)[/tex] at each given [tex]\( x \)[/tex]-value, we find that only the point [tex]\((6.2, 7.4)\)[/tex] lies on the function. Thus, the point on the function is [tex]\((6.2, 7.4)\)[/tex].
