I need help with transformations. This is what my instructions say to do:
Begin by graphing the standard absolute value function f(x)=|x|. Then use transformations of this graph to graphy the given function.
1. g(x)=|x|+3
Wouldn't it just move it up 3 verically?
go across 3 then go up 3
To graph the function g(x)=|x|+3, we need to understand how it is related to the standard absolute value function f(x)=|x|.
The given function g(x)=|x|+3 can be understood as a transformation of the standard absolute value function f(x)=|x|. The transformation in this case is a vertical shift of 3 units upwards.
To graph g(x)=|x|+3, follow these steps:
Step 1: Graph the standard absolute value function f(x)=|x|. This is a V-shaped graph with its vertex at the origin (0, 0) and the two legs extending upward and downward from it.
Step 2: Apply the transformation by shifting the entire graph of f(x)=|x| vertically 3 units upward. To do this, for each point on the graph of f(x)=|x|, add 3 units to the corresponding y-coordinate.
For example, if f(x)=|x| has a point (-2, 2), the corresponding point on g(x)=|x|+3 would be (-2, 5) since 2 + 3 = 5.
Step 3: Plot all the transformed points and connect them with a smooth curve. This will give you the graph of g(x)=|x|+3.
Remember, when graphing absolute value functions, the graph is symmetrical with respect to the y-axis. So, if you have one point on the right side of the y-axis, you will have its symmetrical point on the left side.
By following these steps, you should be able to graph the given function g(x)=|x|+3.