Question

find the following for the function \\(f(x) = 3x^2 + 3x - 4\\).

(a) \\(f(0)\\)
(b) \\(f(4)\\)
(c) \\(f(-4)\\)
(d) \\(f(-x)\\)
(e) \\(-f(x)\\)
(f) \\(f(x + 3)\\)
(g) \\(f(4x)\\)
(h) \\(f(x + h)\\)

Explanation:

Identify the function and input

The given function is:

$$f(x) = 3x^2 + 3x - 4$$

We need to evaluate this function at the input value \(x = 4\).

Substitute the input value

Using the Function Evaluation knowledge point, we replace every occurrence of the variable \(x\) in the function's formula with the number \(4\):

$$f(4) = 3(4)^2 + 3(4) - 4$$

Simplify the expression

We calculate the numerical value step-by-step:

1. Evaluate the exponent:

$$4^2 = 16$$

1. Multiply the terms:

$$3(16) = 48$$

$$3(4) = 12$$

1. Combine the terms:

$$f(4) = 48 + 12 - 4$$

$$f(4) = 60 - 4 = 56$$

Answer:

(b) \(f(4) =\) <blank>56</blank>