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:

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<reasoning>

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:

\[f(4) = 48 + 12 - 4\]
\[f(4) = 60 - 4 = 56\]
</reasoning>

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

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Answer:

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<reasoning>

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:

\[f(4) = 48 + 12 - 4\]
\[f(4) = 60 - 4 = 56\]
</reasoning>

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

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