Graphing Equation

Question

Let f(x)=x+4​ . Graph g(x)=f(4x)​ 

Choose the description of the transformation from the graph of f​ to the graph of g.

Responses

1. The graph of g is a horizontal stretch of the graph of f by a factor of 4
2. The graph of g is a horizontal shrink of the graph of f by a factor of 1/4
3. The graph of g is a vertical stretch of the graph of f by a factor of 4
4. The graph of g​ is a vertical shrink of the graph of f​ by a factor of 1/4

Answer 1

Given a function f(x), a new function g(x)=f(bx), where b is a constant, is a horizontal stretch or horizontal compression of the function f(x)

.

If b>1 then the graph will be compressed by 1/b

If 0<b<1 then the graph will be stretched by 1/b

Graphed: Red is f(x), blue is g(x).

Correct answer: The graph of g is a horizontal shrink of the graph of f by a factor of 1/4