The vertex of the graph of a function describes the point where the function reaches its maximum or minimum value. However, for the given function f(x) = x^3 + 7, we are dealing with a cubic function rather than a quadratic function.
In a cubic function, there isn’t a single vertex like there is for parabolas. Instead, cubic functions can have a point of inflection where the curve changes direction, but they don’t have a maximum or minimum in the same sense. For the function f(x) = x^3 + 7, as x approaches positive or negative infinity, the function continuously increases or decreases.
To analyze the graph further, we notice that the function is centered around the point where x = 0, which gives us f(0) = 0^3 + 7 = 7. This point (0, 7) is where the graph crosses the y-axis and is the local point of interest, but it’s not a vertex.
If you’re interested in the inflection point, it’s located at (0, 7) as well. So in summary, while cubic functions don’t have a vertex, the important point to note is that the function is centered around (0, 7).