Side-by-side tikzpicture (use of axis causes problems)

Question

I am struggling with putting three graphs side-by-side in one line. Every solution I could find caused errors because of the usage of axis.

\begin{tikzpicture}
    \begin{axis}[
                    domain=-10:10,
                    grid=major,
                    xmin=-10, xmax=10,
                    ymin=-10, ymax=10,
                    xlabel={x}, ylabel={y},
                    samples=1000,
                    axis y line=center,
                    axis x line=middle
                ]
        \addplot+[mark=none,color=blue] {1 * abs(x-1) + 0};
    \end{axis}
\end{tikzpicture}

\begin{tikzpicture}
    \begin{axis}[
                    domain=-10:10,
                    grid=major,
                    xmin=-10, xmax=10,
                    ymin=-10, ymax=10,
                    xlabel={x}, ylabel={y},
                    samples=1000,
                    axis y line=center,
                    axis x line=middle
                ]
        \addplot+[mark=none,color=red] {1 * abs(x-0) + 0};
    \end{axis}
\end{tikzpicture}

\begin{tikzpicture}
    \begin{axis}[
                    domain=-10:10,
                    grid=major,
                    xmin=-10, xmax=10,
                    ymin=-10, ymax=10,
                    xlabel={x}, ylabel={y},
                    samples=1000,
                    axis y line=center,
                    axis x line=middle
                ]
        \addplot+[mark=none,color=green] {1 * abs(x+1) + 0};
    \end{axis}
\end{tikzpicture}

I would like to get these three pictures side-by-side in one line including a caption for each of them + a caption for the whole figure. I tried a lot with figures and subfigures etc., but I always got error messages telling me that something is wrong because of the \begin{axis} part. This is how I would like it to look like:

---

EDIT: @martijnn2008 reply to your comment

I just tried that: Caption issue when placing figure side by side - but it doesn't work.

\begin{figure}
    \centering
    \begin{minipage}[t]{.45\textwidth}
        \centering
        \resizebox{0.2\textwidth}{!}{
            \begin{tikzpicture}
                \begin{axis}[
                        domain=-10:10,
                        grid=major,
                        xmin=-10, xmax=10,
                        ymin=-10, ymax=10,
                        xlabel={x}, ylabel={y},
                        samples=1000,
                        axis y line=center,
                        axis x line=middle
                    ]
                    \addplot+[mark=none,color=blue] {1 * abs(x-0) + 0};
                \end{axis}
            \end{tikzpicture}
        }
        \caption{A not.}
    \end{minipage}\hfill

    \begin{minipage}[t]{.45\textwidth}
        \centering
        \resizebox{0.2\textwidth}{!}{
            \begin{tikzpicture}
                \begin{axis}[
                        domain=-10:10,
                        grid=major,
                        xmin=-10, xmax=10,
                        ymin=-10, ymax=10,
                        xlabel={x}, ylabel={y},
                        samples=1000,
                        axis y line=center,
                        axis x line=middle
                    ]
                    \addplot+[mark=none,color=blue] {1 * abs(x-0) + 0};
                \end{axis}
            \end{tikzpicture}
        }
        \caption{A caption.}
    \end{minipage}
    \caption{Lorem Ipsum dolor sit atmet.}
\end{figure}

As you can see in the image, the two graphs are still not in one row. But we have captions now.

Answer 1

Many thanks to @martijnn2008 and @cmhughes! Here is the solution:

\begin{figure}
    \centering
    \begin{minipage}[t]{.50\textwidth}
        \centering
            \begin{tikzpicture}
                \begin{axis}[
                        domain=-10:10,
                        grid=major,
                        xmin=-10, xmax=10,
                        ymin=-10, ymax=10,
                        xlabel={x}, ylabel={y},
                        samples=1000,
                        axis y line=center,
                        axis x line=middle
                    ]
                    \addplot+[mark=none,color=blue] {1 * abs(x-0) + 0};
                \end{axis}
            \end{tikzpicture}

        \caption{$h=0$}
    \end{minipage}\hfill
    \begin{minipage}[t]{.50\textwidth}
        \centering
            \begin{tikzpicture}
                \begin{axis}[
                        domain=-10:10,
                        grid=major,
                        xmin=-10, xmax=10,
                        ymin=-10, ymax=10,
                        xlabel={x}, ylabel={y},
                        samples=1000,
                        axis y line=center,
                        axis x line=middle
                    ]
                    \addplot+[mark=none,color=red] {1 * abs(x-1) + 0};
                \end{axis}
            \end{tikzpicture}
        \caption{$h=1$}
    \end{minipage}
    \caption{$\forall a, h, k \in \mathbb{R}, f(x) = a \mid x-h \mid + k$}
\end{figure}