For the function f(x) = (x − 2)2 + 4, identify the vertex, domain, and range. (2 points)

okay

vertex:(2,4)

domain: (-∞,∞)

range: [4,∞)

Step-by-step explanation:

to find the vertex from the equation

f(x) = (x − 2)² + 4

an easy way is to use the numbers given. so the vertex of this equation is x= 2 (because it is always the opposite of itself in the equation) and y= 4 because the point is going up 4.

to find domain is easy. domain is on the x-axis so the equation is a parabola so it has to points at the same direction. therefore it has a domain that goes from negative infinity to positive infinity.

lastly to find range, which is on the y-axis is to find from where the parabola starts and is pointing, either up or down. in this equation the vertex, which is also the starting point starts at 4 and continues to go on- to infinity.

ps i hope this helps.

guess at question:

a vertical line intersects the graph of g(x,y) = 0 at two points. what conclusion follows about the function f(x) implicitly defined by g(x,f(x)) = 0?

the domain of f(x) cannot include the x coordinate of any such vertical line.

informally, f(x) is not a function, and

g(x,y)=0 cannot be solved for y uniquely.

the relation r = {(x,y) such that g(x,y) = 0} is a function if

for all (a,b) ∊ r and (c,d) ∊ r, a=c implies b=d.

step-by-step explanation:

80° is the measure of gh

step-by-step explanation:

circle f is congruent to circle j

we have two circle with center f and j.

both circles are congruent. the radius of the circle would be equal.

see the attachment for the circle.

we are given ∠efd ≅ ∠gjh

therefore, arc (ed) = arc (gh)     (∴ circle f is congruent to circle j)

but ∠dfe=80°=arc (ed)

therefore, arc (gh) = 80°

thus, 80° is the measure of gh