SOLUTION: Consider the linear function f(x)=A(x-B)+C. Discuss all the changes in the graph as A,B,and C change from positive,negative,zero, as well as, grow smaller or larger. Discuss the do

Algebra ->  College  -> Linear Algebra -> SOLUTION: Consider the linear function f(x)=A(x-B)+C. Discuss all the changes in the graph as A,B,and C change from positive,negative,zero, as well as, grow smaller or larger. Discuss the do      Log On


   

Question 614444: Consider the linear function f(x)=A(x-B)+C. Discuss all the changes in the graph as A,B,and C change from positive,negative,zero, as well as, grow smaller or larger. Discuss the domain and range of linear functions.
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
The best way to see what's going on is to say
+A+=+1+
+B+=+1+
+C+=+1+
Now change A, B, and C to +3, 0, -3 while others stay +1
I will show plots:
This is The equation to start with:
+graph%28+400%2C+400%2C+-5%2C+5%2C+-5%2C+5%2C+x+%29+
This is A being changed:

This is B being changed:
+graph%28+400%2C+400%2C+-5%2C+5%2C+-5%2C+5%2C+x+-+2%2C+x+%2B+1%2C+x+%2B+4+%29+
This is C being changed:
+graph%28+400%2C+400%2C+-5%2C+5%2C+-5%2C+5%2C+x+%2B+2%2C+x+-+1%2C+x+-+4+%29+
As you can see,
Changing A affects the slope and shifts right for positive A, left for negative A
Changing B shifts the line right for positive B, left for negative B
Changing C shifts the line left for positive C, right for negative C