Given the graph of `f(x),` draw the graph each one of the following functions :

(a) `y=f(x)+3 " (b) " y= -f(x)+2`
(c ) `y=f(x+1)-2 " (d) " y= -f(x-1)`
(e ) `y=f(-x) " (f) " y=f(|x|)`
(g) `y=f(1-x)`

Explanation

(a) For `y=f(x)+3,` shift the graph of `y=f(x), 3` units upward.

(b) `y= -f(x) +2`
First graph of `y=f(x)` about x-axis to get `y= -f(x).`

Now, shift the above graph 2 units upward to get `y=2-f(x).`

(c ) `y=f(x+1)-2`
First shift the graph of `y=f(x),` 1 units left to get `y=f(x+1).`

Now shift the above graph 2 units downward to get
`y=f(x+1)-2`.

(d) `y= -f(x-1)`
First shift the graph of `y=f(x), ` 1 unit right to get `y=f(x-1).`

Now, flip the above graph about x- axis to get `y= -f(x-1).`

(e ) `y=f(-x)`
Flip the graph about y-axis to get `y=f(-x).`

(f) `y=f(|x|)`
Neglect the graph of `y=f(x)` for `x lt 0` and take the mirror image of `y=f(x)` for `x gt 0` about y-axis, keeping `y=f(x)` for `x gt 0`.

(g) `y=f(1-x)`
First flip the graph to get `y=f(-x)` as in (e ). Then shift `y=f(-x),` 1 unit left hand side to get `y=(1-x).`