What is the effect on the graph of $f\left(x\right)=|3x-4|$ when it is replaced by $f\left(x\right)+3$?

• A. The graph shifts down by $3$ units.
• B. The graph shifts left by $3$ units.
• C. The graph shifts up by $3$ units.
• D. The graph shifts right by $3$ units.

Answer: (C)

Verified step by step guidance

1. Identify the original function: \(f(x) = |3x - 4|\).
2. Understand that adding a constant outside the function, such as \(f(x) + 3\), affects the vertical position of the graph.
3. Recall that adding a positive number to the function shifts the graph upward by that number of units.
4. Therefore, the transformation \(f(x) + 3\) shifts the entire graph of \(f(x)\) up by 3 units.
5. Note that horizontal shifts occur when the input variable \(x\) is changed inside the function, which is not the case here.