Question

Anybody It's easy!! if correct answered, will give crown.. I'm stuck at this for sooo long.. Anyone please helpppppppp.

What kind of transformation converts the graph of f(x)=2|x|+4 into the graph of g(x)=|x|+2?

reflection across the y-axis
reflection across the x-axis
Vertical stretch
Vertical Shrink

Answer 1

The transformation that converts the graph of f(x)=2|x|+4 into the graph of g(x)=|x|+2 is a Vertical Shrink.

To see this, note that the 2 in f(x) causes a vertical stretch of the absolute value graph. Removing the 2 in g(x) results in a Vertical Shrink of the absolute value graph. The +4 and +2 only cause a vertical shift of the graph.

Answer 2

Answer: Vertical Shrink

Explanation:

The transformation that converts the graph of f(x)=2|x|+4 into the graph of g(x)=|x|+2 is a vertical shrink.

To see why, let's examine each function separately:

• The function f(x) = 2|x| + 4 has an absolute value in its equation, which means it has a "V" shape. The coefficient 2 in front of the absolute value means that the "V" is stretched vertically by a factor of 2. The constant 4 added to the end of the function moves the entire graph up by 4 units.

• The function g(x) = |x| + 2 also has an absolute value in its equation, but without a coefficient in front of it. This means that the "V" shape is not stretched or shrunk vertically. The constant 2 added to the end of the function moves the entire graph up by 2 units.

Therefore, the transformation from f(x) to g(x) involves removing the vertical stretch by dividing the absolute value term by 2. This results in a smaller "V" shape for the graph of g(x), or a vertical shrink.

The answer is:

`$\boxed{\text{Vertical Shrink}}$`