algebra 2a - unit 6: radical equations

consider the graph of function f(x). https://cdstools.flipswitch.com/asset/media/1237263 which function rule represents f(x)?

(3)√x + 2, x ≥ 0

examine the graph of function f(x) https://cdstools.flipswitch.com/asset/media/1237270 which function rule represents f(x)?

-(3)√x+5 + 6

examine the graph of function f(x). https://cdstools.flipswitch.com/asset/media/1237264 which statements are true about the function represented by the graph? select all that apply.

0.5 of 1 the function has no x-intercept and no y-intercept the domain of the function is [2, ∞), and the range of the function is (−∞, −1]

the perimeter of a square can be found using the equation p = 4√a where a represents the area of the square. if the square has a perimeter of 56 inches, what is the area of the square?

196 square inches

find the solutions to the equation (3)√x^2 = 4 choose the correct reason for each numbered statement that is used to solve the equation.

1: given 2: rewrite the expression using a rational exponent. 3: raise both sides of the equation to the reciprocal exponent. 4: simplify

the speed of a carnival ride that spins its passengers around in a circle can be modeled with the following function. s = 4.82√r s represents speed in meters per second, and r represents the length of the radius in meters. if the speed of the ride is 9.64 meters per second, what is the radius of the circular ride?

4 meters

what is the side length of the square if the area is 4x + 12 in.^2?

6 inches

if f(x) = (3)√x-1 + 2, what is the function rule for g(x)?

g(x) = (3)√-1/4x-1 + 2

which rules explain the transformation that takes f(x) to g(x)?

g(x) = (3)√x-3 + 6 g(x) = f(x - 3) + 6

lesson 26

graphing radical function

all done!

have a good day/night.

which graph represents the function that has the rule g(x) = (3)√x-3 + 1?

https://cdstools.flipswitch.com/asset/media/1237255

which graph represents the function that has the rule f(x) = (3)√x+2 + 27?

https://cdstools.flipswitch.com/asset/media/1237259

which graph represents the function that has the rule g(x) = -(3)√x+3 - 4?

https://cdstools.flipswitch.com/asset/media/1237266

which graph shows f(x) and the function g(x) = √x+2 - 4?

https://cdstools.flipswitch.com/asset/media/1237385

which graph shows f(x) and the function g(x) = 5√x-1 + 5?

https://cdstools.flipswitch.com/asset/media/1237390

for the function f(x) = 3√x+4, as x approaches infinity, f(x) approaches _[blank]_. which word or phrase correctly fills in the blank?

infinity

why did joey use the exponent of 1/4 in line 2?

joey needed to rewrite the radical as an exponent to solve the equation, and an exponent of 1/4 is equivalent to the fourth root of a number.

when solved correctly, the equation √4x-8 = x-5 has solutions of x = 3 and x = 11. which, if any, of the solutions are extraneous?

only x = 3 is extraneous

when solved correctly, the equation √-2x+12 = x-6 has solutions of x = 6 and x = 4. which, if any, of the solutions are extraneous?

only x = 4 is extraneous

when solved correctly, the equation √x = 2 - x has solutions of x = 1 and x = 4. which, if any, of the solutions are extraneous?

only x = 4 is extraneous

why did phoebe use the exponent of 1/3 in line 2?

phoebe needed to rewrite the radical as an exponent to solve the equation, and an exponent of 1/3 is equivalent to the cube root of a number.

lesson 27

radical equations and inequalities in context

lesson 25

solving radical equations

what are the domain and range of the portion of the function that applies to this situation?

the domain is (0, ∞), and the range is (0, ∞)

maura wants to buy fencing to install around a square garden in her yard. the perimeter of the garden can be represented by the equation p = 4√a where a is the area of the garden. what are the domain and range of the part of the function that represents this situation?

the domain is x > 0, and the range is y > 0

consider the function f(x) = 3√x-3 + 1. which statements about f(x) are true? select all that apply.

the function has a minimum, which is 1 the domain of the function is [3, ∞), and the range of the function is [1, ∞) the function starts at point (3, 1), and as x approaches infinity, f(x) approaches infinity.

examine the graph of function f(x). https://cdstools.flipswitch.com/asset/media/1237253 which statements are true about the function represented by the graph? select all that apply.

the function has no maximum the function has a minimum of −3 the function starts from the point (−4, −3), and as x approaches infinity, f(x) approaches infinity.

consider the radical function g(x) = (3)√x+2 + 2 which statement about g(x) is true?

the function has no maximum and no minimum.

consider the radical function g(x) = -(3)√x+3 - 4 which statements about g(x) are true? select all that apply.

the function has no maximum and no minimum. the interval of both the domain and range of the function is all real numbers. as x approaches negative infinity, f(x) approaches infinity, and as x approaches infinity, f(x) approaches negative infinity.

consider the radical function g(x) = (3)√x+4 which statements about g(x) are true? select all that apply.

the function has no maximum and no minimum. the interval of both the domain and range of the function is all real numbers. as x approaches negative infinity, f(x) approaches negative infinity, and as x approaches infinity, f(x) approaches infinity.

examine the graph of function f(x). https://cdstools.flipswitch.com/asset/media/1237254 which statements are true about the function represented by the graph? select all that apply.

the function has no minimum. the function has no maximum as x approaches negative infinity, f(x) approaches infinity, and as x approaches infinity, f(x) approaches negative infinity.

what are the intercepts of the function f(x) = √3x-12 - 15?

the function has no y-intercept but has an x-intercept of (79, 0)

the function f(x) = (3)√x-1 + 2 is dilated to become f'(x) = -3(3)√x-1 - 6. which statement describes the transformation?

the function is reflected over the x-axis and is stretched away from the x-axis by a factor of 3

the function f(x) = (3)√x-1 + 2 is dilated to become f'(x) = (3)√-3x-1 + 2. which statement describes the transformation?

the function is reflected over the y-axis and is compressed toward the y-axis by a factor of 1/3

the function f(x) = (3)√x-9 + 4, f'(x) = (3)√x+5 - 1. which statement describes the transformation?

the function moves 14 units to the left and 5 units downward.

the function f(x) = (4)√x+4 - 2 is translated to become f'(x) = (4)√x+1 - 2? which statement describes the transformation?

the function moves 3 units to the right

tobin is purchasing a cube-shaped water tank. the side width of the cube can be represented by the equation..... is (0, 0) a valid point in the context of this situation? why or why not?

the point is not valid in terms of the context because a cube can't have a volume or side width of 0

is (0, 0) a valid point in terms of the context of the situation? why or why not?

the point is not valid in terms of the context because the garden can't have an area of 0 square feet.

examine the graph of function f(x) https://cdstools.flipswitch.com/asset/media/1237265 which statements about f(x) are true? select all that apply.

the range of the function is (−∞, ∞) the domain of the function is (−∞, ∞) the x-intercept is (−11, 0), and the y-intercept is (0, 3.4)

consider the graph of f(x). https://cdstools.flipswitch.com/asset/media/1237253 which statements about f(x) are true? select all that apply.

the range of the function is [−3, ∞) the domain of the function is [−4, ∞) the x-intercept is (5, 0), and the y-intercept is (0, −1)

consider the graph of function f(x) https://cdstools.flipswitch.com/asset/media/1237254 which statements about f(x) are true? select all that apply.

the range of the function is all real numbers. the domain of the function is all real numbers the x-intercept is (12, 0) and the y-intercept is (0, 3.6)

lesson 28

transformations of radical functions

jodi wants to get an aquarium that is shaped like a cube. the width of each side can be represented by the equation w = (3)√v, where v represents the volume of the tank. the filter she has cleans up to 27 cubic feet of water. which inequality represents the width of the tank that best suits her filter?

w ≤ 3 feet

find the solution(s) to the radical equation 2(4)√x^3 - 4 = 12

x = 16

find the solution(s) to the equation √7x-10 = x

x = 2 and x = 5

find the solution(s) to the equation 3√x+1 = 15

x = 24

find the valid solution(s) to the equation x = √x+6

x = 3

what is the value of x in the given equation? √7x-12 = x

x = 3 and x = 4

what is the value of x in the given equation? √2x+15 - x = 0

x = 5

what does the point (8, 2) represent in the context of this situation?

a tank with a volume of 8 cubic feet has a side width of 2 feet.

which statement correctly describes anna's mistake in the solution process?

anna should have raised both sides of the equation to the power of 2 in line 3 because this keeps the equality.

examine the graphs of function f(x) and g(x). https://cdstools.flipswitch.com/asset/media/1237394 using the dilation formula g(x) = a ⋅ f(1/bx), which equation gives the correct information according to the transformation from f(x) to g(x)?

b = -4