Question

I need help with this equation 20 points help quick

Answer 1

The equation of the graph after translating one unit to the left is;

`y = \left | (x)/(2) - (3)/(2) \right |+3`

Explanation:

The given equation is
`y = \left | (1)/(2)\cdot x - 2 \right |+3`

We note that minimum value of y = 3, where 1/2·x - 2 = 0 and x = 4

Therefore, in moving one unit to the left, we have at the y-intercept where slope of the graph has become inverted (reflection of the real graph) we add one to the x value as follows;

`y = \left | (1)/(2)\cdot (x+1) - 2 \right |+3 = \left | (x)/(2) + (1)/(2) - 2 \right |+3 = \left | (x)/(2) - (3)/(2) \right |+3`

The equation of the graph becomes;

`y = \left | (x)/(2) - (3)/(2) \right |+3`.