Question

Given f(x)=3x+5 describe how the graph of g compares with the graph of f. g(x)=3(0.1)+5

Answer 1

The given function f(x) is:

$f(x)=3x+5$

And the other given function g(x) is:

$g(x)=3(0.1x)+5$

g(x) in comparison with f(x) has the next transformation:

1. g(x)=f(bx): g(x)=3(0.1x)+5. This is a horizontal stretch: the x-coordinates will change as:

$(x,y)\rightarrow(\frac{x}{0.1},y)$

This is the graph of both functions:

The red-one is f(x) and the blue-one is g(x).

Then for example when the coordinates of f(x) are (1,8) for g(x) the coordinates will be:

$(\frac{1}{0.01},8)=(10,8)$

Then, the slope of f(x) has a greater value than the slope of g(x), since the change on the x-axis is bigger in the g(x) graph for the.