At vero eos et accusamus et iusto odio dignissimos ducimus qui blanditiis praesentium voluptatum deleniti atque corrupti quos dolores et quas molestias excepturi sint occaecati cupiditate non provident, similique sunt in culpa qui officia deserunt mollitia animi, id est laborum et dolorum fuga. Et harum quidem rerum facilis est et expedita distinctio. Nam libero tempore, cum soluta nobis est eligendi optio cumque nihil impedit quo minus id quod maxime placeat facere possimus, omnis voluptas assumenda est, omnis dolor repellendus. Itaque earum rerum hic tenetur a sapiente delectus, ut aut reiciendis voluptatibus maiores alias consequatur aut perferendis doloribus asperiores repellat.
what is the range on f(x)=|x+7| ?
i think i'm not sure somehow my teacher got (- infinity, 0] and i have no idea what he did
what is the range of f(x)=|anything| ? what values can an absolute value take on?
im sorry i'm so confused i know the domain is all reals because nothing limits it but i also thought hte range would be like all reals as well yet he gave us a diff answer so im unsure what to do
can |x| be negative?
so then the range is not all reals, is it? it can't be negative, the least it can be is zero. It can be as big as you want though by putting in larger and larger x. so the range of f(x)=|x+7| is [0,infty) , agreed?
well even if x is a negative number wouldnt it not matter because the absolute value makes it postivie?
right, so that means it \[|x|\ge0\]like I said, the LEAST it can be is zero. Hence the range is from zero to positive infinity\[[0,\infty)\] So far so good ?
OH okay gotcha now
now what about\[f(x)=-|x|\]if |x| is always positive, then -|x| is always negative. The MOST it can be is zero. We can make f(x) very negative (as negative as we want in fact) by putting in very large negative or positive x. Hence the range is\[(-\infty,0]\](I hope you see that the 7 and 4 change nothing, only the fact that the 4 is negative matters) Make sense now?
yes it does thank you so much you're a life saver
happy to help :)