\text{a) Given } f(x) = 3x^2 + x - 5
f(0) = 3(0)^2 + 0 - 5 = -5
(0, -5)
\text{b) Given } f(x) = 3x^2 + x - 5
f(5) = 3(5)^2 + 5 - 5 = 3(25) + 5 - 5 = 75 + 5 - 5 = 75
(5,75)
\text{c) Given } f(x) = 3x^2 + x - 5
f(x+1) = 3(x+1)^2 + (x+1) - 5
= 3(x^2 + 2x + 1) + x + 1 - 5
= 3x^2 + 6x + 3 + x + 1 - 5
= 3x^2 + 7x - 1
\left(x+1,3x^2+7x-1\right)