11. How many of the following four equations has a graph that does not pass through the origin?
$$
y=x^{4}+1 \quad y=x^{4}+x \quad y=x^{4}+x^{2} \quad y=x^{4}+x^{3}
$$

A 0
B 1
C 2
D 3
E 4
Solution
B

The origin has coordinates $(0,0)$. Thus it is the point where $x=0$ and $y=0$. It follows that the graph of an equation passes through the origin if the equation shows that $y=0$ when $x=0$.
Now, when $x=0$, the values of $x^{4}+1, x^{4}+x, x^{4}+x^{2}$ and $x^{4}+x^{3}$ are $1,0,0$ and 0 , respectively.
Hence, of the given equations, $y=x^{4}+1$ is the only one whose graph does not pass through the origin.