Let's determine the values of f(x) based on the given x-values using the following function:
[tex]\text{ f\lparen x\rparen = }\frac{\text{ x}^2\text{ + x - 42}}{\text{ x - 7}}[/tex]At x = -9,
[tex]\text{ f\lparen-9\rparen= }\frac{(-9)^2\text{ + \lparen-9\rparen- 42 }}{-9\text{ - 7}}\text{ = }\frac{81\text{ - 9 - 42}}{-9\text{ - 7}}\text{ = }\frac{30}{-16}\text{ = -}\frac{15}{8}\text{ \lparen Simplified\rparen}[/tex]At x = -8,
[tex]\text{ f\lparen-8\rparen = }\frac{(-8)^2\text{ + \lparen-8\rparen - 42}}{-8\text{ - 7}}\text{ = }\frac{64\text{ - 8 - 42}}{-8\text{ - 7}}\text{ = }\frac{14}{-15}\text{ = -}\frac{14}{15}[/tex]At x = -1,
[tex]\text{ f\lparen-1\rparen = }\frac{(-1)^2\text{ +}(-1)\text{ - 42}}{-1\text{ - 7}}\text{ = }\frac{1\text{ - 1 - 42}}{-1\text{ - 7}}\text{ = }\frac{-42}{-8}\text{ = }\frac{21}{4}\text{ \lparen Simplified\rparen}[/tex]At x = 15/2,
[tex]\text{ f\lparen}\frac{15}{2})\text{ = }\frac{(\frac{15}{2})^2\text{ + \lparen}\frac{15}{2})\text{ - 42}}{\frac{15}{2}\text{ - 7}}\text{ = }\frac{\frac{225}{4}+\frac{30}{4}\text{ - }\frac{168}{4}}{\frac{30}{4}\text{ - }\frac{28}{4}}\text{ = }\frac{225\text{ + 30 - 168}}{30\text{ - 28}}\text{ = }\frac{87}{2}[/tex]At x = 10,
[tex]\text{ f\lparen10\rparen = }\frac{(10)^2\text{ + \lparen10\rparen - 42}}{\text{ 10 - 7}}\text{ = }\frac{\text{ 100 + 10 - 42}}{10\text{ - 7}}\text{ = }\frac{68}{3}[/tex]In Summary,
At x = -9, f(-9) = -15/8
At x = -8, f(-8) = -14/15
At x = -1, f(-1) = 21/4
At x = 15/2, f(15/2) = 87/2
At x = 10, f(10) = 68/3
