Yes, you do need to mount the partition but that's not the only issue. Look at the parted output, you have no filesystem on sdf1. Next to primary partition type it doesn't say anything more, the filesystem column is empty.

This is a new disk and you still have no data on it, right?
If that is right, format it with:
sudo mkfs.ext4 /dev/sdf1
After that adjust fstab to mount /dev/sdf1 not /dev/sdf. And make sure the mount point you are trying to use exists first, if it doesn't you need to create it the first time you want to use it.

That should sort it out.

If you did have data on the disk, don't format it, it will destroy it. You will need to investigate why the filesystem is missing if it was formatted once and has data on it.