Question

State whether the graph of f(x)=(x^3+15x^2+56x)/7 has infinite discontinuity, jump discontinuity, point discontinuity, or is continuous.

Answer 1

The function f(x) = (x^3 + 15x^2 + 56x)/7 is continuous for all values of x.

Step-by-step explanation:

To determine the nature of the graph of the function f(x) = (x^3 + 15x^2 + 56x)/7, we need to analyze its continuity.

A function is continuous if it is defined for all values of x and has no breaks, jumps, or holes in its graph.

In this case, the function is a rational function, which is continuous everywhere except where the denominator is equal to zero. Set the denominator, 7, equal to zero and solve for x.

Since there is no solution, the rational function has no discontinuities and is continuous for all values of x.

Therefore, the graph of f(x) = (x^3 + 15x^2 + 56x)/7 is continuous.

Answer 2

The correct answer among the choices given is the last option. The function f(x)=(x^3+15x^2+56x)/7 has a continuous graph. A continuous function is a a function for which sufficiently small changes in the input result in small changes in the output.