Radical Word Problems

Post Malone is designing a new tattoo in the shape of a radical function. The base shape of the tattoo is given by the function f(x) = sqrt(x). If he wants to shift the tattoo design 3 units to the right and 2 units up, what is the new function that represents the transformed tattoo design?

• f(x) = sqrt(x+3) - 2

• f(x) = sqrt(x-3) + 2

• f(x) = sqrt(x+3) + 2

• f(x) = sqrt(x-3) - 2

Answer explanation

To shift the function f(x) = sqrt(x) 3 units right, we replace x with (x-3). To shift it 2 units up, we add 2. Thus, the new function is f(x) = sqrt(x-3) + 2, which is incorrect. The correct transformation is f(x) = sqrt(x+3) + 2.

Mrs. Slate, a math teacher, is a huge Post Malone fan. She notices that the number of Post's Instagram followers over time can be modeled by the function f(x) = sqrt(2x), where x is the number of months since January 2023. In which month will Post's follower count reach 28 million?

• Month 392

• Month 64

• Month 28

• Month 16

Answer explanation

To find when Post's followers reach 28 million, set f(x) = sqrt(2x) = 28. Squaring both sides gives 2x = 784, so x = 392. Thus, it will take 392 months since January 2023.

Post Malone's latest album sales can be represented by the function h(x) = sqrt(5x), where x is the number of weeks since the album's release and h(x) represents the number of albums sold in thousands. What is the domain of this function, and what does it represent in the context of album sales?

• x >= -1, weeks before album release

• x >= 0, weeks after album release

• x >= 1, months after album release

Answer explanation

The function h(x) = sqrt(5x) is defined for x >= 0, as negative weeks do not make sense in this context. Thus, the correct choice is x >= 0, weeks after album release, representing the time since the album was launched.

Mrs. Slate is organizing a Post Malone concert at her school. The stage design includes a backdrop shaped like a radical function. The original function is f(x) = sqrt(x). If Mrs. Slate wants to stretch the design horizontally by a factor of 2 and reflect it over the x-axis, what is the new function that represents the transformed backdrop?

• f(x) = sqrt(2x)

• f(x) = -sqrt(2x)

• f(x) = -sqrt(x/2)

• f(x) = (1/2)sqrt(-x)

Answer explanation

To stretch horizontally by a factor of 2, replace x with x/2. Reflecting over the x-axis changes the sign. Thus, f(x) = -sqrt(x/2) is the transformed function, making it the correct choice.

Post Malone's tattoo artist charges according to the function C(x) = 100sqrt(x), where x is the number of hours spent on a tattoo and C(x) is the cost in dollars. If Post Malone has budgeted $500 for his next tattoo, how many hours can the tattoo artist spend on it?

• 4 hours

• 9 hours

• 25 hours

• 49 hours

Answer explanation

To find the hours, set C(x) = 500: 100sqrt(x) = 500. Dividing by 100 gives sqrt(x) = 5. Squaring both sides results in x = 25. Thus, the tattoo artist can spend 25 hours.

Mrs. Slate and Post Malone are collaborating on a math-themed music video. They want to incorporate a radical function that starts at the origin, passes through the point (4, 2), and opens upward. Find a function of the form f(x) = a(sqrt(x)) that satisfies these conditions.

• f(x) = (1/2)sqrt(x)

• f(x) = 2sqrt(x)

• f(x) = sqrt(x)

• f(x) = (1/4)sqrt(x)

Answer explanation

To find the function f(x) = a(sqrt(x)), we use the point (4, 2). Plugging in, we get 2 = a(sqrt(4)) => 2 = 2a => a = 1. Thus, f(x) = sqrt(x) satisfies all conditions, including starting at the origin and passing through (4, 2).

Post Malone is planning a new stage design for his concert tour. The design is based on the function g(x) = sqrt(x). If he wants to compress the design vertically by a factor of 1/3 and shift it 4 units to the left, what is the new function that represents the transformed stage design?

• g(x) = (1/3)sqrt(x+4)

• g(x) = (1/3)sqrt(x-4)

• g(x) = 3sqrt(x+4)

• g(x) = 3sqrt(x-4)

Mrs. Slate is creating a math puzzle for her students using Post Malone's album sales data. The sales are modeled by the function s(x) = sqrt(3x), where x is the number of weeks since the album's release. If the sales reach 15,000 albums, how many weeks have passed since the release?

• Week 25

• Week 75

• Week 5

• Week 45

Post Malone's new merchandise line is modeled by the function m(x) = sqrt(x) + 5, where x is the number of days since the launch and m(x) is the number of items sold in hundreds. If he wants to adjust the model to reflect a decrease of 3 items sold per day, what is the new function?

• m(x) = sqrt(x) + 2

• m(x) = sqrt(x) - 3

• m(x) = sqrt(x) + 8

• m(x) = sqrt(x) - 5