Radical Functions: Graphing and Finding Extraneous Solutions

A swimming pool is being filled with water. The volume of water in the pool can be modeled by the equation V = √(h), where h is the height of the water in meters. If the volume is 25 cubic meters, what is the height of the water? Graph the function and check for extraneous solutions.

• 25 meters

• 100 meters

• 50 meters

• 625 meters

A car travels a distance of d kilometers in t hours. The relationship can be modeled by the equation d = √(t). If the distance traveled is 36 kilometers, what is the time taken? Graph the function and identify any extraneous solutions.

• 36 hours

• 1296 hours

• 12 hours

• 144 hours

A rectangular garden has a length that is 3 meters longer than its width. The area of the garden can be expressed as A = √(w(w + 3)). If the area is 50 square meters, find the width and graph the function to check for extraneous solutions.

• Width is 5 meters.

• Width is 8 meters.

• Width is 10 meters.

• Width is approximately 6.79 meters.

A rock is dropped from a height of h meters. The time it takes to hit the ground can be modeled by the equation t = √(h/4.9). If the rock takes 2 seconds to hit the ground, what was the height from which it was dropped? Graph the function and identify any extraneous solutions.

• 9.8 meters

• 19.6 meters

• 24.5 meters

• 15.0 meters

A rectangular pool has a width of x meters and a length of x + 5 meters. The area of the pool is 60 square meters. Write the equation for the area and solve for x. Graph the function and check for extraneous solutions.

• x = 3

• x = 5

• x = 0

• x = 10

A cyclist travels a distance of d kilometers in t hours. The relationship can be modeled by the equation d = √(t + 1). If the distance traveled is 9 kilometers, what is the time taken? Graph the function and identify any extraneous solutions.

• 20 hours

• 5 hours

• 80 hours

• 50 hours

A square garden has a perimeter of P meters. The relationship can be modeled by the equation P = 4√(s), where s is the length of a side. If the perimeter is 64 meters, find the length of a side and graph the function to check for extraneous solutions.

• 64 meters

• 256 meters

• 16 meters

• 32 meters

A scientist is measuring the growth of bacteria. The number of bacteria can be modeled by the equation N = √(t + 1), where t is time in hours. If the number of bacteria is 36, how long has it been? Graph the function and identify any extraneous solutions.

• 500 hours

• 12 hours

• 1295 hours

• 100 hours

A rectangular field has a length that is twice its width. The area of the field can be expressed as A = √(2w^2). If the area is 72 square meters, find the width and graph the function to check for extraneous solutions.

• 10 meters

• 6 meters

• 8 meters

• 4 meters