1. **Problem statement:** Given the function $f(x) = x^2 + 1$, find the values of $f(0)$, $f(5)$, $f(-5)$, $f(-x)$, $-f(x)$, $f(x+3)$, $f(4x)$, and $f(x+h)$. 2. **Formula:** The function is defined as $f(x) = x^2 + 1$. To find $f(a)$ for any input $a$, substitute $a$ into the function: $f(a) = a^2 + 1$. 3. **Evaluate each part:** (a) $f(0) = 0^2 + 1 = 0 + 1 = 1$. (b) $f(5) = 5^2 + 1 = 25 + 1 = 26$. (c) $f(-5) = (-5)^2 + 1 = 25 + 1 = 26$. (d) $f(-x) = (-x)^2 + 1 = x^2 + 1$. (e) $-f(x) = -(x^2 + 1) = -x^2 - 1$. (f) $f(x+3) = (x+3)^2 + 1 = x^2 + 6x + 9 + 1 = x^2 + 6x + 10$. (g) $f(4x) = (4x)^2 + 1 = 16x^2 + 1$. (h) $f(x+h) = (x+h)^2 + 1 = x^2 + 2xh + h^2 + 1$. 4. **Summary:** - $f(0) = 1$ - $f(5) = 26$ - $f(-5) = 26$ - $f(-x) = x^2 + 1$ - $-f(x) = -x^2 - 1$ - $f(x+3) = x^2 + 6x + 10$ - $f(4x) = 16x^2 + 1$ - $f(x+h) = x^2 + 2xh + h^2 + 1$