Question

Which is the graph of f(x)=|x| reflected across the x-axis, translated 3 units left, 4 units up, and dilated by a factor of 4?

Answer 1

The graph of the equation is attached

How to get the equation and the graph

The equation is gotten form the parent equation f(x) = |x|

The sequence of transformation is as follows

f(x) = |x|: parent function

f(x) = -|x|: reflection across the x-axis

f(x) = -|x + 3| : translation 3 units to the left

f(x) = -|x + 3| + 4: translation 4 units to up

f(x) = -4|x + 3| + 4: translation 4 units to up

Answer 2

The equation after the transformation is f(x) = -4|x + 3| + 16 and the graph is attached

How to determine the graph and the equation after the transformation

From the question, we have the following parameters that can be used in our computation:

f(x) = |x|

Also, we have the sequence of transformation to be

Reflection across the x-axis

This gives

f(x) = -|x|

Next, we have a translation by 3 units to the left

This gives

f(x) = -|x + 3|

Next, we have a translation by 4 units up

So, we have

f(x) = -|x + 3| + 4:

Laslty, we have a dilation by a scale factor of 4

This gives

f(x) = -4|x + 3| + 16

Hence, the equation after the transformation is f(x) = -4|x + 3| + 16 and the graph is attached