Part A)
Recall that:
1) The function represented by the graph of the function f(x) translated vertically n units up and horizontally m units left is:
2) The function represented by the graph of the function f(x) reflected over the x-axis is:
Now, notice that g(x) is the function f(x) reflected over the x-axis and then translated vertically 6 units up and horizontally 4 units left.
Answer Part A:
Options B, C, and D.
Part B) To graph g(x) we will reflect the graph of f(x) over the x-axis and then we will translate it vertically 6 units up and horizontally 4 units left.
We know that the graph of f(x)=|x| is:
The above graph reflected over the x-axis is:
Finally, the above graph translated vertically 6 units up and horizontally 4 units left is:
Answer part B:
