#1
Which of the following represents a radical function?
f(x) = x^2 + 3
f(x) = √(x + 2)
f(x) = |x|
f(x) = 2x - 5
#2
Which of the following is the parent function of radical functions?
f(x) = x
f(x) = x^2
f(x) = √x
f(x) = |x|
#3
What is the vertex of the function f(x) = √(x + 3) - 2?
(-3, -2)
(3, 2)
(0, -2)
(-3, 0)
#4
Which of the following transformations does the function y = √x undergo if changed to y = √(x + 3)?
Horizontal shift 3 units to the right
Horizontal shift 3 units to the left
Vertical shift 3 units up
Vertical shift 3 units down
#5
Which of the following transformations does the function y = √(x - 1) undergo if changed to y = √(x - 1) - 2?
Horizontal shift 1 unit to the right and vertical shift 2 units down
Vertical shift 1 unit to the left and horizontal shift 2 units down
Horizontal shift 1 unit to the left and vertical shift 2 units down
Vertical shift 1 unit to the right and horizontal shift 2 units up
#6
What is the domain of the function f(x) = √(3x + 4)?
All real numbers
x ≥ -4/3
x ≥ 4/3
x < -4/3
#7
Which transformation does the function y = √x undergo if the function is changed to y = √(x - 2)?
Reflection over the x-axis
Horizontal shift 2 units to the right
Vertical shift 2 units up
Vertical shift 2 units down
#8
What is the range of the function f(x) = √(4 - x^2)?
All real numbers
y ≥ 0
y ≤ 0
y > 0
#9
Which of the following represents the graph of the function f(x) = √(x - 1) + 2?
A horizontal shift of 1 unit to the left and a vertical shift of 2 units up from the graph of y = √x.
A vertical shift of 1 unit to the right and a vertical shift of 2 units down from the graph of y = √x.
A vertical shift of 1 unit to the left and a vertical shift of 2 units up from the graph of y = √x.
A horizontal shift of 1 unit to the right and a vertical shift of 2 units up from the graph of y = √x.
#10
Which of the following transformations does the function y = √(x + 4) undergo if changed to y = √(x + 4) + 3?
Vertical shift 4 units down
Vertical shift 3 units up
Horizontal shift 4 units to the left
Vertical shift 3 units down
#11
What is the range of the function f(x) = √(x^2 + 4x + 4)?
All real numbers
y ≥ 0
y ≤ 0
y > 0
#12
What is the range of the function f(x) = √(x^2 + 9)?
All real numbers
y ≥ 0
y ≤ 0
y > 0
#13
What is the inverse function of f(x) = √(x + 5)?
f^-1(x) = (x - 5)^2
f^-1(x) = x^2 - 5
f^-1(x) = x^2 + 5
f^-1(x) = (x - 5)^2 + 5
#14
What is the range of the function f(x) = √(x^2 - 16)?
All real numbers
y ≥ 0
y ≤ 0
y > 0
#15
What is the inverse function of f(x) = √(4x + 1)?
f^-1(x) = (x^2 - 1)/4
f^-1(x) = (x^2 + 1)/4
f^-1(x) = (x^2 - 1)/16
f^-1(x) = (x^2 + 1)/16
#16
What is the end behavior of the function f(x) = √(x^3 - 2x^2 + 5)?
As x approaches negative infinity, f(x) approaches negative infinity, and as x approaches positive infinity, f(x) approaches positive infinity.
As x approaches negative infinity, f(x) approaches positive infinity, and as x approaches positive infinity, f(x) approaches negative infinity.
As x approaches negative infinity, f(x) approaches negative infinity, and as x approaches positive infinity, f(x) approaches negative infinity.
As x approaches negative infinity, f(x) approaches positive infinity, and as x approaches positive infinity, f(x) approaches positive infinity.
#17
What are the asymptotes of the function f(x) = √(x^2 + 4x + 3)?
x = -3, x = -1
x = -1, x = 3
y = -3, y = -1
y = -1, y = 3
#18
Which of the following best describes the behavior of the function f(x) = √(x^2 + 1) as x approaches infinity?
The function approaches positive infinity.
The function approaches negative infinity.
The function oscillates between positive and negative infinity.
The function approaches a finite limit.
#19
What are the x-intercepts of the function f(x) = √(x^2 - 16)?
x = -4, x = 4
x = -16, x = 16
x = -2, x = 2
x = -8, x = 8
#20
Which of the following is the correct limit as x approaches negative infinity for the function f(x) = √(4x^2 - x + 3)?
#21
What is the domain of the function f(x) = √(x^2 - 9)/(x - 3)?
x ≠ 3
All real numbers
x > 3
x < 3
#22
What is the limit as x approaches infinity for the function f(x) = √(x^2 - 4x + 5)?
#23
Which of the following functions is not continuous everywhere?
f(x) = √(x^2 + 1)
f(x) = √(x^2 - 4x + 4)
f(x) = √(x^2 - 9)
f(x) = √(x^2 - 25)
#24
What is the limit as x approaches negative infinity for the function f(x) = √(x^2 + 9)?
#25
Which of the following functions has no real zeros?
f(x) = √(x^2 + 1)
f(x) = √(x^2 - 4x + 4)
f(x) = √(x^2 - 9)
f(x) = √(x^2 - 25)