Question

Which of the following are characteristics of the graph of the square root
parent function? Check all that apply.

Answer 1

Answer:

C.  It is in Quadrant I

D.  It starts at the origin

Step-by-step explanation:

Parent function:  $f(x)=\sqrt{x}$

Domain: set of all possible input values (x-values)

As the square root of a negative number does not exist in the set of Real Numbers, the domain for the parent function is:

• Solution:  x ≥ 0
• Interval notation:  [0, ∞)

Range: set of all possible output values (y-values)

As the domain of the parent function is x ≥ 0, the range will be:

• Solution:  f(x) ≥ 0
• Interval notation:  [0, ∞)

As the range and domain both begin at zero, the graph of the parent function starts at the origin (0, 0).

Quadrant: a region of the Cartesian plane formed when the x-axis and y-axis intersect each other.

Quadrant I:  (x, y)

Quadrant II:  (-x, y)

Quadrant III: (-x, -y)

Quadrant IV:  (x, -y)

Therefore, as the range and domain of the parent function are positive, the graph is in Quadrant I.