Understanding and Analyzing Radical Functions Quiz

Test your knowledge on radical functions with questions on domain, range, transformations, limits, and more.

Practice Learn Test

Which of the following represents a radical function?

f(x) = x^2 + 3

f(x) = √(x + 2)

f(x) = |x|

f(x) = 2x - 5

Which of the following is the parent function of radical functions?

f(x) = x

f(x) = x^2

f(x) = √x

f(x) = |x|

What is the vertex of the function f(x) = √(x + 3) - 2?

(-3, -2)

(3, 2)

(0, -2)

(-3, 0)

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

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

What is the domain of the function f(x) = √(3x + 4)?

All real numbers

x ≥ -4/3

x ≥ 4/3

x < -4/3

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

What is the range of the function f(x) = √(4 - x^2)?

All real numbers

y ≥ 0

y ≤ 0

y > 0

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 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.

#12

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

#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.

The function approaches negative infinity.

The function oscillates between positive and negative infinity.

The function approaches a finite limit.

#14

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

#15

Which of the following is the correct limit as x approaches negative infinity for the function f(x) = √(4x^2 - x + 3)?

∞

Undefined