SW #2 Evaluate the function 1) f(x) = x² - x - 12 a. f(-3) c. f(x-2) b. f(-5) d. f(x-1) 2) g(x) = x² - 3x + 9 a. g(4) c. g(2x+5) b. g(x-5)

Let's evaluate the given functions step-by-step.

Function f(x) = x^2 - x - 12
a. f(-3) : Substitute x = − 3 into the function:
f ( − 3 ) = ( − 3 ) 2 − ( − 3 ) − 12 = 9 + 3 − 12 = 0
c. f(x-2) : Substitute x = x − 2 into the function:
f ( x − 2 ) = ( x − 2 ) 2 − ( x − 2 ) − 12 = ( x 2 − 4 x + 4 ) − x + 2 − 12 = x 2 − 5 x − 6
b. f(-5) : Substitute x = − 5 into the function:
f ( − 5 ) = ( − 5 ) 2 − ( − 5 ) − 12 = 25 + 5 − 12 = 18
d. f(x-1) : Substitute x = x − 1 into the function:
f ( x − 1 ) = ( x − 1 ) 2 − ( x − 1 ) − 12 = ( x 2 − 2 x + 1 ) − x + 1 − 12 = x 2 − 3 x − 10

Function g(x) = x^2 - 3x + 9
a. g(4) : Substitute x = 4 into the function:
g ( 4 ) = 4 2 − 3 ( 4 ) + 9 = 16 − 12 + 9 = 13
c. g(2x+5) : Substitute x = 2 x + 5 into the function:
g ( 2 x + 5 ) = ( 2 x + 5 ) 2 − 3 ( 2 x + 5 ) + 9 = ( 4 x 2 + 20 x + 25 ) − ( 6 x + 15 ) + 9 = 4 x 2 + 14 x + 19
b. g(x-5) : Substitute x = x − 5 into the function:
g ( x − 5 ) = ( x − 5 ) 2 − 3 ( x − 5 ) + 9 = ( x 2 − 10 x + 25 ) − ( 3 x − 15 ) + 9 = x 2 − 13 x + 49


Each step involves substituting the given values into the functions and simplifying the expressions to find the result.

Answered by AvaCharlotteMiller | 2025-07-22