Differences in brain metabolism as measured by FDG-PET in prodromal and early Alzheimer's disease (AD) have been consistently observed, with a characteristic parietotemporal hypometabolic pattern. However, exploration of brain metabolic correlates of more nuanced measures of cognitive function has been rare, particularly in larger samples. We analyzed the relationship between resting brain metabolism and memory and executive functioning within diagnostic group on a voxel-wise basis in 86 people with AD, 185 people with mild cognitive impairment (MCI), and 86 healthy controls (HC) from the Alzheimer's Disease Neuroimaging Initiative (ADNI). We found positive associations within AD and MCI but not in HC. For MCI and AD, impaired executive functioning was associated with reduced parietotemporal metabolism, suggesting a pattern consistent with known AD-related hypometabolism. These associations suggest that decreased metabolic activity in the parietal and temporal lobes may underlie the executive function deficits in AD and MCI. For memory, hypometabolism in similar regions of the parietal and temporal lobes were significantly associated with reduced performance in the MCI group. However, for the AD group, memory performance was significantly associated with metabolism in frontal and orbitofrontal areas, suggesting the possibility of compensatory metabolic activity in these areas. Overall, the associations between brain metabolism and cognition in this study suggest the importance of parietal and temporal lobar regions in memory and executive function in the early stages of disease and an increased importance of frontal regions for memory with increasing impairment.