Question

Write the equations after translating the graph of y=|1/2x-2|+3. One unit to the left

Answer 1

Answer:

$g(x) = |\frac{1}{2}x - \frac{3}{2} | + 3$

Step-by-step explanation:

Given

$y = |\frac{1}{2}x - 2| + 3$

Required

Translate the above one unit to the left

Replace y with f(x)

$y = |\frac{1}{2}x - 2| + 3$

$f(x) = |\frac{1}{2}x - 2| + 3$

When an absolute function is translated to the left, the resulting function is

$g(x) = f(x - h)$

Because it is been translated 1 unit to the left, h = -1

$g(x) = f(x - (-1))$

$g(x) = f(x + 1)$

Calculating $f(x+1)$

$f(x+1) = |\frac{1}{2}(x+1) - 2| + 3$

Open bracket

$f(x+1) = |\frac{1}{2}x + \frac{1}{2} - 2| + 3$

$f(x+1) = |\frac{1}{2}x + \frac{1-4}{2} | + 3$

$f(x+1) = |\frac{1}{2}x + \frac{-3}{2} | + 3$

$f(x+1) = |\frac{1}{2}x - \frac{3}{2} | + 3$

Recall that

$g(x) = f(x + 1)$

Hence;

$g(x) = |\frac{1}{2}x - \frac{3}{2} | + 3$