Write the equation that models the function described. Shifts the parent function, y=log_(0.5)x 3 units up y=log_(0.5)(x-3) y=3+log_(0.5)x y=3log_(0.5)x y=log_(0.5)(x+3) y=-3+log_(0.5)x

## Step 1<br />The problem involves the transformation of a logarithmic function. The parent function given is \(y = \log_{0.5}x\). The task is to shift this function 3 units up.<br /><br />## Step 2<br />The general form of a logarithmic function is \(y = \log_b(x - h) + k\), where \(h\) and \(k\) represent the horizontal and vertical shifts respectively.<br /><br />## Step 3<br />In this case, the function is shifted 3 units up, which means \(k = 3\). There is no horizontal shift, so \(h = 0\).<br /><br />## Step 4<br />Substituting \(h = 0\) and \(k = 3\) into the general form of the logarithmic function, we get \(y = \log_{0.5}(x - 0) + 3\), which simplifies to \(y = \log_{0.5}x + 3\).