at which root does the graph of f(x)=(x+4)^6(x+7)^5 cross the x-axis ?

Answer:
-7
Step-by-step explanation:
The equation is simplified so there are two possible answers here, -4 and -7
There is a root where y = 0 and x = a number
At -4 and -7 y = 0
However at -4 the function bounces since the (x+4) is raised to the 6th power.
When you have an even power, the function bounces at the x-axis, and when you have an odd power the function goes through the x-axis.
Since you can only choose one answer, the logical answer would be -7.
At x = -7, y = 0 and the function crosses the x-axis.
At x = -4, y = 0 but the function bounces on the x-axis.
The logical answer here is -7.
The graph crosses the x-axis at x = -7
The roots of a function are the zeros of the function
The function of the graph is given as:
[tex]f(x) =(x+4)^6(x+7)^5[/tex]
In the above equation, the roots of the functions and their corresponding multiplicities are:
The graph will cross the x-axis, when the multiplicity is odd
The root, -7 has an odd multiplicity.
Hence, the graph crosses the x-axis at x = -7
Read more about roots and multiplicities at:
https://brainly.com/question/2833285