We are given the function f(x)=x+1. When we transform this function to be g(x)=f(2x), we need to multiply only the values of x — the input — by 2. Let's write an explicit form for g(x).
g(x)=f(2x) ⇒ g(x)=2x+1Note that this is a horizontal shrink by a factor of 12. We can identify the slopes and y-intercepts by comparing the equations to the slope-intercept form. The x-intercept is not as simple. We need to set each equation equal to 0 and solve for x.
& 0=x+1 && ⇔ x=-1
& 0=2x+1 && ⇔ x=-1/2
Let's do a table of values of the features of each function.
Feature
f(x)
g(x)
Slope
1
2
y-intercept
1
1
x-intercept
-1
-1/2
This transformation doubled the slope, halved the x-intercept, and left the y-intercept unchanged.
