I understand how the forget gate works.
My understanding of the forget gate:

A sigmoid function is used to make each of the gate tensor's values $\Gamma\_f^{<t>}$ range from 0 to 1.
The forget gate $\Gamma\_f^{<t>}$ has the same dimensions as the previous cell state $c^{⟨t−1⟩}$. This means that the two can be multiplied together, element-wise. Multiplying the tensors $\Gamma\_f^{<t>}\*c^{⟨t−1⟩}$ is like applying a mask over the previous cell state. If a single value in $\Gamma\_f^{<t>}$ is 0 or close to 0, then the product is close to 0.

What I don't understand is the purpose of the update gate and how does it achieve its purpose?