#1
Which of the following represents a radical function?
f(x) = √(x + 2)
ExplanationSquare root function
#2
Which of the following is the parent function of radical functions?
f(x) = √x
ExplanationThe square root function
#3
What is the vertex of the function f(x) = √(x + 3) - 2?
(-3, -2)
ExplanationVertex at (-3, -2)
#4
Which of the following transformations does the function y = √x undergo if changed to y = √(x + 3)?
Horizontal shift 3 units to the left
ExplanationHorizontal shift to the left by 3 units
#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
ExplanationHorizontal shift right by 1 unit and down by 2 units
#6
What is the domain of the function f(x) = √(3x + 4)?
x ≥ -4/3
ExplanationDomain includes all real numbers greater than or equal to -4/3
#7
Which transformation does the function y = √x undergo if the function is changed to y = √(x - 2)?
Horizontal shift 2 units to the right
ExplanationHorizontal shift to the right by 2 units
#8
What is the range of the function f(x) = √(4 - x^2)?
y ≥ 0
ExplanationRange includes all real numbers greater than or equal to 0
#9
Which of the following represents the graph of the function f(x) = √(x - 1) + 2?
A vertical shift of 1 unit to the left and a vertical shift of 2 units up from the graph of y = √x.
ExplanationVertical shift to the left by 1 unit and up by 2 units
#10
Which of the following transformations does the function y = √(x + 4) undergo if changed to y = √(x + 4) + 3?
Vertical shift 3 units up
ExplanationVertical shift up by 3 units
#11
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.
ExplanationApproaches negative infinity as x → -∞ and positive infinity as x → ∞
#12
What are the asymptotes of the function f(x) = √(x^2 + 4x + 3)?
x = -1, x = 3
ExplanationVertical asymptotes at x = -1 and x = 3
#13
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.
ExplanationFunction approaches positive infinity as x → ∞
#14
What are the x-intercepts of the function f(x) = √(x^2 - 16)?
x = -4, x = 4
Explanationx-intercepts at -4 and 4
#15
Which of the following is the correct limit as x approaches negative infinity for the function f(x) = √(4x^2 - x + 3)?
2
ExplanationLimit is 2 as x → -∞