The domain of g(x) is -1< x < 9
What is the domain of g(x - 4)
I know the Domain: ?< x <?
i know the graph shifts left by four. But I do not remember how to find the domain to be honest.
would it be -5 < x < 5.
nvm i found the answer. I derped hard and forgot it needed to shift right. so it would be 3<x<3
To find the domain of the function g(x - 4), we need to consider two factors: the original domain of g(x) and the effect of the transformation.
First, let's review the original domain of g(x), which is given as -1 < x < 9. This means that x can take any value between -1 and 9, excluding the endpoints.
Now, let's look at the transformation g(x - 4). The function g(x - 4) involves shifting the graph of g(x) horizontally to the right by 4 units. Since the shift is to the right, the x-values are increasing by 4.
To determine the new domain, we need to consider how the original domain is affected by this shift. In this case, since we are shifting to the right, the new domain will shift along with the graph. Each x-value in the original domain will increase by 4.
Applying this shift, the new domain can be obtained by adding 4 to the original domain endpoints. Thus, the domain of g(x - 4) is -1 + 4 < x + 4 < 9 + 4, which simplifies to 3 < x < 13.
Therefore, the domain of g(x - 4) is 3 < x < 13.