Which statement describes the graph of f(x) = 4x7 + 40x6 + 100x5?
the graph crosses the x axis at x = 0 and touches the x axis at x = 5.
the graph touches the x axis at x = 0 and crosses the x axis at x = 5.
the graph crosses the x axis at x = 0 and touches the x axis at x = –5.
the graph touches the x axis at x = 0 and crosses the x axis at x = –5.

First, factorize the function f(x):

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When f(x)=0, you get that

.

This means that the graph intersects x-axis at point (0,0) and (-5,0). But:

1. since the degree at term is odd, point (0,0) is x-intercept;

2. since the degree at term is even, point (-5,0) is tangent point (see attached graph of the function).

The graph crosses the x axis at x = 0 and touches the x axis at x = –5.

what