True or False? Given the function \( f(x)=x^{3} \), the graph of the function \( h(x)=f(x)+10 \) is the graph of \( f(x) \) shifted 10 units vertically upward: Option \#1: True Option \#2: False (1 point) The best answer to the question is Option \# \( \square \).
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The Deep Dive
True! When you have a function like \( f(x) = x^3 \) and you modify it by adding a constant, such as +10, the overall effect is to lift the entire graph vertically. So, the new function \( h(x) = f(x) + 10 \) results in every point on the original graph moving up by 10 units. It’s like giving your graph a little boost into the sky! Not only is this concept useful in math, but it also appears in real-world situations, like when you’re adjusting the height of a roller coaster or even setting things on different levels in a video game. When you're having fun with functions, remember that adding a constant will shift the graph up or down, while multiplying will stretch or compress it!