Question

i need help with this equation 20 points help quick

Answer 1

Answer:

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

$y = \left | \dfrac{x}{2} - \dfrac{3}{2} \right |+3$

Step-by-step explanation:

The given equation is $y = \left | \dfrac{1}{2}\cdot x - 2 \right |+3$

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;

$y = \left | \dfrac{1}{2}\cdot (x+1) - 2 \right |+3 = \left | \dfrac{x}{2} + \dfrac{1}{2} - 2 \right |+3 = \left | \dfrac{x}{2} - \dfrac{3}{2} \right |+3$

The equation of the graph becomes;

$y = \left | \dfrac{x}{2} - \dfrac{3}{2} \right |+3$.