Question

find the domain and range of the graphs:

y=2^x
y=x^2-4
y=x^2+4x+3
y=sqrt(x-2)
y=sqrt(4-x^2)
y=|x+3|-2

Answer 1

all of them?

Answer 2

first one
domain, all real numbers. you can raise 2 to any power.
range, positive numbers. 2 to any power is positive

Answer 3

second one
domain, all real numbers. you can square anything and add 4 to the result
range, all numbers greater than or equal to -4. any numbers squared us at least 0, so once you subtract 4 the least it can be is -4

Answer 4

thanks so much for your help so far (:

Answer 5

third one
domain is all real numbers. it is a polynomial
range, the graph is a parabola that faces up. the vertex is (-2,-1) so minimum is -1 and range is
\[[-1,\infty)\]

Answer 6

fourth one
\[\sqrt{x-2}\] you have to make sure that
\[x-2\geq 0\] so
\[x\geq 2\] is the domain.
range is \[[0,\infty)\] since the radical sign indicates the positive root.

Answer 7

fifth one
\[\sqrt{4-x^2}\] is the only tricky one. RANGE is
\[[0,\infty)\] for the same reason as last one.

Answer 8

if you know that this is the graph of the upper half of a circle with center at the origin and radius 2, then you know that the range is
\[[-2,2]\]
if you do not know that, then you have to solve
\[4-x^2\geq0\] which is not too hard but you have to be careful. it is a parabola that faces down with zeros at -2 and 2, so it will be positive between the zero (draw a mental picture)
in any case the domain is
\[-2\leq x\leq 2\]

Answer 9

last one
domian, all real numbers because you can take the absolute value of anything
range
\[[-2,\infty)\] because the absolute value is a least 0, so whole thing is at least -2

Answer 10

hope reasoning is clear

Answer 11

thannks so freaking much!! :D