What kind of transformation converts the graph of $f(x)=|x+5|-10$ into the graph of $g(x)=|x+10|-4$ ? translation 5 units left and 6 inits up translation 5 units right and 6 units up translation 5 units right and 6 units down translation 5 units left and 6 units down
Solution
Step 1 ：The transformation from \(f(x)\) to \(g(x)\) involves two steps: a horizontal shift and a vertical shift.
Step 2 ：The horizontal shift is determined by the change in the value inside the absolute value function, while the vertical shift is determined by the change in the constant term outside the absolute value function.
Step 3 ：In this case, the value inside the absolute value function changes from \(x+5\) to \(x+10\), which corresponds to a shift of 5 units to the left.
Step 4 ：The constant term outside the absolute value function changes from -10 to -4, which corresponds to a shift of 6 units up.
Step 5 ：Therefore, the transformation that converts the graph of \(f(x)\) into the graph of \(g(x)\) is a translation 5 units left and 6 units up.
Step 6 ：Final Answer: The transformation that converts the graph of \(f(x)\) into the graph of \(g(x)\) is a \(\boxed{\text{translation 5 units left and 6 units up}}\).
