a We have to compare the given function f(x)=2|x|-3 with the parent function f(x)=|x|. Since our function was multiplied by 2 and 3 is subtracted from it, there were 2 transformations made. Let's draw the graphs and try to identify what exactly happened.
From the graph, we can see that the parent function f(x)=|x| was vertically stretched to the function f(x)=2|x|. Then, it was shifted down by 3 units and became f(x)=2|x|-3. Therefore, the given function contains a vertical translation.
b We have to compare the given function f(x)=(x-8)^2 with the parent function f(x)=x^2. Since the only difference between the functions is -8, there will be only one transformation. Let's sketch both functions in order to identify it.
From the graph, we can see that the function f(x)=(x-8)^2 is shifted 8 units right. Therefore, it contains a horizontal translation.
c We have to compare the given function f(x)=|x+2|+4 with the parent function f(x)=|x|. Since our function has 2 added inside the absolute value and 4 added outside the absolute value, there were 2 transformations made. Let's sketch the situation and try to identify what happened.
From the graph, we can see that the parent function f(x)=|x| was shifted 2 units left to f(x)=|x+2|. Next, it was shifted 4 units up and became f(x)=|x+2|+4. This means that the function contains both vertical and horizontal translations.
d We have to compare the given function f(x)=4x^2 with the parent function f(x)=x^2. Since our function is only multiplied by 4, there will be one transformation done. Let's sketch the situation and try to identify what happened.
From the graph we can see that the given function f(x)=4x^2 is vertically stretched, but is not shifted anywhere. Therefore, the function contains neither vertical nor horizontal translations.
