Square Root Function
Graph y = √(x+1) and state the domain and range.
Domain: { x | x >= -1}
Range: { y | y >= 0}
(4-√(5))^2
21-8√(5)
√(x+4) = 6
32
If the two legs are 5 and 12, what is the hypotenuse of the right triangle?
13
If the height of the right triangle is 5, the base is 12, and the hypotenuse is 13. Find the trigonometric ratios for the angle A across from the side 12.
sin A = 12/13
cos A = 5/13
tan A = 12/5
Graph y = 2√(x-2) + 2 and state the domain and range.
Domain : { x | x >= 2}
Range: {y | y >= 2 }
2√(3) * 3√(12)
36
√(3x) = 2
4/3
If one leg has length 2 and the hypotenuse is 8, find the length of the other leg.
2√(15)
If the base of the triangle if 4 and the hypotenuse is 5, find the trigonometric ratios for the angle A across from the base.
sin A = 4/5
cos A = 3/5
tan A = 4/3
Compare y = 1/2√(x+1) to the parent graph y = √(x).
It is less steep and shifted to the left 1.
√(20ab^3)
2b √(5ab)
√(x+4) = x-8
12
Could 4, 5, 6 be the lengths of the sides of a right triangle?
No
If the height of the right triangle is 3 feet and the angle across from the height is 30 degrees, find the length of the hypotenuse.
sin 30 = 0.5
cos 30 = 0.866
tan 30 = 0.577
6 ft
Compare y = 2√(x) -3 to the parent graph y = √(x).
It is more steep and shifted down 3.
5/(√(7) + 6)
(5√(7) -30)/(-29)
√(3x-14) + x= 6
5
Could 7, 24, 25 be the lengths of the sides of a right triangle?
Yes
If the base of a right triangle is 10 and angle next to the base is 50 degrees, find the lengths of the other sides.
12 feet and 15.6 feet
Compare y = -2√(x + 2) -4 to the parent graph y = √(x).
It is upside down, more steep, left 2 and down 4.
2√(1/2) + 2√(2) -√(8)
√(2)
10 + 2√(x) = 0
No solution
A ladder is leaning on a building. The base of the ladder is 20 feet from the building and the ladder reaches up 30 feet on the building. How long is the ladder?
36 feet
If the height of a right triangle is 6 and the base is 10, find the measure of the angle next to the side of length 10.
31 degrees