# Chapter 2, Functions - Section 2.6 - Transformations of Functions - 2.6 Exercises - Page 243: 50 The given function can be written as: $y=-|x|+2$ RECALL: (1) The function $y=f(x-h)$ involves a horizontal shift of $h$ units to the right of the parent function $f(x)$ when $h\gt0$. The function involves a horizontal shift of $|h|$ units to the left when $h \lt0$. (2) The function $y=-f(x)$ involves a reflection about the x-axis of the parent function $f(x)$. (3) The function $y=a\cdot f(x)$ involves a vertical stretch of the parent function $f(x)$ when $a\gt1$, and involves a vertical compression when $0 \lt a \lt 1$. (4) The function $y=f(x)+c$ involves a vertical shift of $c$ units upward of the parent function $f(x)$ when $c \gt 0$. The function will involve a vertical shift of $|c|$ units downward when $c \lt 0$. The parent function of the given function is $f(x)=|x|$. The given function can be written $y=-f(x)+2$ where $f(x)$ is the parent function. Thus, the graph of the given function involves: (i) a reflection about the x-axis, (ii) a shift of $2$ units upward of the parent function $f(x)=|x|$. Therefore, to graph the given function: (1) Graph the parent function $y=|x|$ . (Refer to the red graph in the attached image below) (2) Reflect the graph of the parent function about the x-axis. (Refer to the orange graph in the attached image below.) (3) Shift the graph in Step (2) two units upward. (Refer to the blue graph in the attached image in the answer part above.) 