Question

What type of transformation takes the graph of f(x)=|x|f(x)=|x| to the graph of g(x)=2.5|x|g(x)=2.5|x|? vertical shift down of 2.5 vertical stretch by a factor of 2.5 vertical compression by a factor of 2.5 vertical shift up of 2.5

Answer 1

vertical stretch by a factor of 2.5

Answer 2

When you apply to the graph of the function $y=f(x)$ following transformations

• vertical shift by a factor a;
• vertical compression by a factor a;
• vertical shift up a units;
• vertical shift down a units,

then you will get the function

• $y=a\cdot f(x),$ where $|a|>1;$
• $y=a\cdot f(x),$ where $0<|a|<1;$
• $y=f(x)+a;$
• $y=f(x)-a.$

In your case, the graph of the function $y=|x|$ was vertically shifted by a factor of 2.5 to form the graph of the function $y=2.5|x|.$

Answer: correct choice is B