1. A multi-point auto-focus digital camera, comprising: an image-capturing element that receives an image through a photographic lens and that outputs an image signal corresponding to the image; a focal point detection device that detects a focal point adjustment state of the photographic lens in each focal point detection region of a plurality of focal point detection regions based on the image signal outputted from the image-capturing element with the plurality of focal point detection regions being arranged at predetermined positions in a photographic field; an image trimming section that trims part of the image signal to create a trimmed image signal; a display device that displays the image signal outputted from the image-capturing element, the trimmed image signal created by the image trimming section, and at least one of the focal point detection regions; a region control section that sets focal point detection regions included in a trimming range among the plurality of focal point detection regions as selectable focal point detection regions according to the trimming range of the trimmed image signal; an operation member that is manually operated by a user to select a focal point detection region from the selectable focal point detection regions; and a focal point adjustment device that carries out focal point adjustment of the photographic lens based on focal point detection results for the focal point detection regions that have been selected by the operation member, wherein the region control section limits the selectable focal point detection regions to include a region in a central portion and at least one region that is included in the trimming range and that is disposed outside the central, portion; the region control section changes size and positions of the plurality of focal point detection regions arranged at the predetermined positions so that all of the plurality of focal point detection regions are disposed in the trimming range and are set as the selectable focal point detection regions; and the display device displays the focal point detection regions whose size and positions are changed after trimming by the image trimming section so that a number of the focal point detection regions displayed after the trimming remains the same as a number of the focal point detection regions displayed by the display device before the trimming.