Examining the given functions, we can identify their slopes m and y-intercepts b.
f(x)= x-1& ⇔ f(x)= 1x+(-1)
g(x)=3x-3& ⇔ g(x)= 3x+(-3)
Let's organize this information in a table.
Function
m
rise/run
b
y-intercept
f(x)=x+(-1)
1
1/1
-1
(0,-1)
g(x)=3x+(-3)
3
3/1
-3
(0,-3)
To graph any function in slope-intercept form, start by plotting the y-intercept and then use the slope to find another point. We will do this for both functions.
Describe the Transformation
Looking at our graph, we see that each point of g is three times further away from the x-axis than f.
This type of transformation is called a vertical stretch. It occurs when the entire function is multiplied by a factor greater than 1. In our case it is 3.
g(x)=3f(x)
We can check our transformation by substituting f(x)=x-1 into this equation.
