Evaluate the function at each specified
value of the independent variable and simplify

Evaluating the function is just replacing the "x" (or the "t" in the second case) by the value that we want:

1) q(x) = 1/(x^2 - 9)

 a) q(0) = 1/(0^2 - 9) = 1/(-9) = - 1/9

 b) q(3) = 1/(3^2 - 9) = 1/(9 - 9) = 1/0 = indetermined, we could think this as:

 c) q(y + 3) = 1/( (y + 3)^2 - 9) = 1/(y^2 + 6*y + 9 - 9) = 1/(y^2 + 6*y)

2) q(t) = (2*t^2 + 3)/t^2

 a) q(2) =  (2*2^2 + 3)/2^2 = (2*4 + 3)/4 = 11/4

 b) q(0) = (2*0^2 + 3)/0^2 = 3/0

  Again, we can not divide by zero, this is simmilar to the case 1.b

 c) q(-x) = (2*(-x)^2 + 3)/(-x)^2 = (2*x^2 + 3)/x^2

step-by-step explanation:

no, her answer is not correct.   we square the lengths of all sides and then determine whether the pythagorean theorem holds here:

9² + 15² = 306.   this is not equal to the square of the longest side ( that square being 395.   answer c is correct.