Assignment: Radical Functions

Multiple-Choice Questions

1. Select the best description of a radical function:

A. a function that involves a radical or root with the variable is in the index
B. a function that involves a radical or root and a variable in the radicand or under the root sign
C. a function that involves a root sign and the value under the root sign that always has the restriction that it must be greater than zero
D. a function that has a root sign in it

2. The population of grasshoppers in a certain area, in thousands, will increase according to the following function.

G(x) = 3 √(2x - 1) + 15

What is the range?
A. y ≥ 15
B. y ≤ 15
C. x ≥ ½
D. x ≥- ½

3. The domain and range of the function f(x) = -2 √(x - 3)

A. x ≥ 3 and f(x) ≤ 0
B. x ≥ 3 and f(x) ≥ 0
C x ≤ 3 and f(x) ≤ 0
D. x ≤ 3 and f(x) ≥ 0

Numeric Response 1

The y-coordinate of the "endpoint" of the graph of y = 4 √(2 - x) + 3 is

4. If f(x) = -2x² + 18, then the range of y = 4 √(f(x))

A. 0 ≤ y ≤ 12 √2

B. y ≤ 12 √ 2

C. 0 ≤ y ≤ 12

D. y ≤ 12

5. The solution to the radical equation √(x - 1) = √(5 - x) may be determined by finding

A. the x-coordinate of the point of intersection of the graphs of y = √(x - 1) and y = √(5 - x)

B. the x-intercept of y = √(x - 1) + √(5 - x)

C. the y-coordinate of the point of intersection of the graphs of y = √(x - 1) and y = √(5 - x)

D. the y-intercept of y = √(x - 1) + √(5 - x)

Numeric Response 2

Given f(x) = 2x² - 6 , then, to the nearest hundredth, the positive x-value that gives the smallest value of y = √f(x) is

6. Select the interval for which y = √(x² - 25) is undefined.

A. x > 5, x < -5

B. -5 < x < 5

C. x > 5

D. x < -5

7. Determine the solution(s) of 8 = 13 - √(16 - 9x) and indicate the restrictions on the equation.

A. x = 1, x ≥- 16/9

B. x = 1, x ≥- 16/9

C. x = 1, x ≤ -16 9

D. x =- 1, x ≤ 16/9

Numeric Response 3

When solving the radical equation 8 = x - √(x -6), the "extraneous" root is

Use the following information to answer multiple-choice questions 8 and 9.

The time, t in seconds, it takes a pendulum to complete one back and forth swing can be determined by the equation t = 0.32
of the pendulum in inches.

8. Determine the length of the pendulum if it takes 1.1 seconds to make a complete back and forth swing.

A. 11. 82 inches

B. 10.8 inches

C 9.12 inches

D. 10.82 inches

9. A clock manufacturer has an adjustable length pendulum with the shortest length pendulum being 7 inches and the longest length pendulum being 11.5 inches. Determine the range of the function in this particular case.

A. 0.847 ≤ t ≤ 1.085

B. 0.847 ≤ t ≤ 0.966

C 0.966 ≤ t ≤ 1.085

D. 0.32 ≤ t ≤ 1.085

Part 2: Written Response

1. If y = f(x) and f(x) = 2x + 5, then the graph of y = f(x) and y =√f(x) will have two common points. One common point is the x-intercept. Determine the other common point.

2. a. Express the side length of a square as a function of its area.

b. Construct a table of values and a graph to illustrate the relationship.

3. Compare the domains of the functions f(x) = √x and g(x) = 2√(x + 3) - 5 .

Which value in the function g(x) affected the domain of f(x)?

4. a. Graph the function f(x) = 4x², x ≥ 0 and its inverse. Show all work and state any restrictions.

b. Determine the inverse of the function f (x) = (1/2)√x. State any restrictions and explain.

c. Explain how the answers to parts a) and b) are related.

5. a. Sketch the graphs of y = f(x) and y = √f(x) where f(x) = -3x + 6.

b. State any invariant points.

c. Explain how mapping from a linear function can assist in graphing the square root of that linear function.

6. A roof truss is designed such that the vertical measurement from inside beam to inside beam is 2 ft 6 in.

Determine a function for the horizontal measurement (d) of the truss.