When given the function f(x)=x3 , which of the following properties should the graph display?(1 point) Responses A graph that is linear. A graph that is linear. A graph that is only concave up. A graph that is only concave up. A graph that is only concave down. A graph that is only concave down. A graph that has a portion that is concave up and a portion that is concave down.

1 answer

The function \( f(x) = x^3 \) is a cubic function. The graph of this function will display the following properties:

  • It is not linear; it is a cubic curve.
  • It is not only concave up or concave down.

Instead, the graph of \( f(x) = x^3 \) has a point of inflection at \( x = 0 \). For values of \( x < 0 \), the graph is concave down, and for values of \( x > 0 \), the graph is concave up.

Therefore, the correct response is: A graph that has a portion that is concave up and a portion that is concave down.