Question

Graph the parent function f(x)=|x|? Graph the translated function g(x)=|x+3|-4 on same grid. B) Use f(x)=|x|. f(x) is shifted left 5 units and shifted up 2 to create g(x). Write the equation g(x)_______.

Answer 1

Given:

The parent function |x| is a modulus function.

The mod function is defined as:

`|x|=\begin{cases}x,x\ge0 \\ -x,x<0\end{cases}`

The points on the graph for this function will be (0,0) , (1,1), (-1,1),...etc

Hence, the graph will be drawn as:

Now, the graph of g(x) = |x+3|-4 is drawn by shifting graph of |x| 3 units to the left and 4 units down.

The graph is shown below,

Now, to obtain the graph g(x) that is shifted 5 units left and 2 units up is given by the equation:

`g(x)=|x+5|+2`