What transformations have occurred to create g(x) ? Select all that apply. f(x)=x g(x)=-4f(x) Translation down 4 units Translation left 4 units Vertical Compression (less steep) Reflection D Vertical Stretch (Steeper)

## Step 1<br />The function \(g(x)\) is derived from the function \(f(x)\) by multiplying it by -4. This operation involves two transformations:<br /><br />### **Reflection**<br />Multiplying a function by -1 reflects the graph of the function across the x-axis. In this case, the negative sign in front of the 4 in \(g(x)=-4f(x)\) indicates a reflection.<br /><br />### **Vertical Stretch**<br />Multiplying a function by a factor greater than 1 (in this case, 4) stretches the graph of the function vertically. The factor of 4 in \(g(x)=-4f(x)\) indicates a vertical stretch.<br /><br />## Step 2<br />The other options, such as translation down 4 units, translation left 4 units, and vertical compression (less steep), do not apply in this case. These transformations would require different operations, such as adding or subtracting a constant from the function or multiplying by a factor less than 1.