Question

PartA)What are the transformations are needed in in order to obtain the graph of G(x) from the graph of f(x) Select all that applyPartB) Graph g(x)

Answer 1

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:

$f(x+m)+n\text{.}$

2) The function represented by the graph of the function f(x) reflected over the x-axis is:

$-f(x)\text{.}$

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: