00:01
But if we want to sketch this graph 3x minus 2 minus 3, what we can do, instead of just arbitrary plugging in some numbers, we can use its parent function, which we actually sketched in number 13 here.
00:16
And we can use that along with some transformations to kind of help us out a little bit.
00:22
So notice here on the left, it's like we start with f of x, and then on the right side, this is going to become f of x because we have.
00:31
Have 3 to the x and the x essentially just got replaced by x minus 2 and then we just subtract 3 on the outside so remember this x minus 2 on the inside is selling us shift um 2 units and we're going to go to the right because on the inside it's always the opposite of what i normally want to say it is and then on the outside well that's going to be vertical changes so it would be up or down since we're adding so it's still a shift but now is going to be down 3 units so we can just come over here and first make our new chart so the x values we're just going to add two to all them so it becomes zero one two three and four and then for the outputs we're just going to subtract three from all of them so this is going to become negative 2 .8 repeating 0 .3 repeating is going to become negative 2 .6 repeating 1 is going to become negative 2 3 is going to become 0 and then 9 is going to become 7 and then we can just go in and plot these or again you can just go ahead and move all of these 2 to the right and then 3 down so 1 2 1 2 1 2 3 1 2 1 2 3 1 2 1 2 3 and then 1 2 1 2 3 and then 1 2 one, two, three, and then the next one would be kind of there.
02:08
All right, and then we could just go ahead and connect all of that...