Question

The graph of f and g are given. Find a formula for the function g.

Short answer

$g\left(x\right)=|x+1|+2$

Step-by-step solution

Step 1. Concept of Horizontal and Vertical shift.

To graph $y=f(x-c)$, shifts the graph $y=f\left(x\right)$to the right c units

And, to graph$y=f(x+c)$ shifts the graph$y=f\left(x\right)$ to the left c units

Adding a constant to a function shifts the graph upward or downward if the constant is positive or negative respectively.

Step 2. Given condition.

Given equation is

$f\left(x\right)=\left|x\right|$; And the graph of $g\left(x\right)$is

Step 3. Determining the formula for the function g.

The graph shifts left 1 unit

So, $c=1$

Then graph shifts upward by the 2 units,

So,$c=2$

Therefore,$g\left(x\right)=|x+1|+2$