Cho hàm $m$ có đồ thị như hình vẽ. Có bao nhiêu giá trị nguyên của...

Đặt $y=g\left( x \right)=f\left( x \right)+m$.
Ta có:
$\begin{aligned}
& \left\{ \begin{aligned}
& \underset{\left[ 0;2 \right]}{\mathop{\min }} f\left( x \right)=-2 \\
& \underset{\left[ 0;2 \right]}{\mathop{\max }} f\left( x \right)=2 \\
\end{aligned} \right.\Rightarrow \left\{ \begin{aligned}
& \underset{\left[ 0;2 \right]}{\mathop{\min }} g\left( x \right)=m-2 \\
& \underset{\left[ 0;2 \right]}{\mathop{\max }} g\left( x \right)=m+2 \\
\end{aligned} \right. \\
& \Rightarrow \underset{\left[ 0;2 \right]}{\mathop{\max }} \left| g\left( x \right) \right|=\max \left\{ \left| m+2 \right|;\left| m-2 \right| \right\} \\
& \Leftrightarrow \left[ \begin{aligned}
& \left\{ \begin{aligned}
& \left| m+2 \right|=4 \\
& \left| m+2 \right|>\left| m-2 \right| \\
\end{aligned} \right. \\
& \left\{ \begin{aligned}
& \left| m-2 \right|=4 \\
& \left| m-2 \right|>\left| m+2 \right| \\
\end{aligned} \right. \\
\end{aligned} \right.\Leftrightarrow m=\pm 2 \\
\end{aligned}$