Your y-intercepts are correct.
y = x^3 + x^2 + 7
Look at the leading term, x^3.
As x approaches infinity, x^3 also approaches infinity. Right: y approaches infinity.
As x approaches negative infinity, x^3 also approaches negative infinity. Left: y approaches negative infinity.
y = -x^4 + 9
Look at -x^4.
If you just think of x^4 (without the negative sign) for a moment, you realize that x^4 approaches infinity both as x approaches infinity and negative infinity. Since 4, the exponent of x, is even, x^4 is never negative and approaches infinity at both ends.
Now think of what the negative sign does. -x^4 is 0 or negative. It is never positive. -x^4 approaches negative infinity at both ends. The constant 9 just translates the graph of y = -x^4 9 units up, but the end behavior at both ends is still to approach negative infinity.
y = x^5 + x^2 + 7x + 1
The leading term has an odd power of x, so follow what I wrote about the first function.
y = x^100
This is like y = x^4. The function approaches infinity at both ends. You have an even power of x and no negative sign like you had in the second function.
