Cho hàm m có đồ thị như hình vẽ. Có bao nhiêu

* Hướng dẫn giải

Đáp án D

Đặt $y=g\left(x\right)=f\left(x\right)+m$.

Ta có:

$\begin{array}{l}\left\{\begin{array}{l}\underset{\left[0;2\right]}{\min }f\left(x\right)=-2\\ \underset{\left[0;2\right]}{\max }f\left(x\right)=2\end{array}\right.\Rightarrow \left\{\begin{array}{l}\underset{\left[0;2\right]}{\min }g\left(x\right)=m-2\\ \underset{\left[0;2\right]}{\max }g\left(x\right)=m+2\end{array}\right.\\ \Rightarrow \underset{\left[0;2\right]}{\max }\left|g\left(x\right)\right|=\max \left\{\left|m+2\right|;\left|m-2\right|\right\}\\ \iff \left[\begin{array}{l}\left\{\begin{array}{l}\left|m+2\right|=4\\ \left|m+2\right|>\left|m-2\right|\end{array}\right.\\ \left\{\begin{array}{l}\left|m-2\right|=4\\ \left|m-2\right|>\left|m+2\right|\end{array}\right.\end{array}\right.\iff m=\pm 2\end{array}$