EXPLANATION :
From the problem, we have the function :
[tex]f(x)=6x^4+5x^3-7x^2+3[/tex]
We will focus on the leading term which is 6x^4
For the left behavior, substitute a negative number to 6x^4
A negative number raised to a power of 4 will give a positive number.
And a positive number multiplied by 6 is also a positive number.
Therefore, the left behavior of the function goes up.
For the right behavior, substitute a positive number to 6x^4
A positive number raised to a power of 4 will give a positive number.
And a positive number multiplied by 6 is also a positive number.
Therefore, the right behavior of the function goes up.
ANSWER :
The answer is Rises to the left and rises to the right
