Question

which parent functions have reflective symmetry?
square root
linear
greatest integer
cubic
rational/reciprocal
quadratic
absolute value
exponential

Explanation:

• Square Root: \( y = \sqrt{x} \) has domain \( x \geq 0 \), not symmetric over y - axis or origin (for reflection).
• Linear: \( y = x \) (a linear function) is symmetric about the origin (reflective symmetry over origin). \( y = mx + b \) with \( b

eq0 \) is not, but the parent linear function \( y = x \) is.

• Greatest Integer: \( y=\lfloor x

floor \) is a step - function, no reflective symmetry.

• Cubic: Parent cubic function \( y = x^{3} \) is symmetric about the origin (odd function, so reflective symmetry over origin).
• Rational/Reciprocal: Parent reciprocal function \( y=\frac{1}{x} \) is symmetric about the origin (odd function).
• Quadratic: Parent quadratic function \( y = x^{2} \) is symmetric about the y - axis (reflective symmetry over y - axis).
• Absolute Value: Parent absolute value function \( y=\vert x\vert \) is symmetric about the y - axis.
• Exponential: \( y = a^{x} \) (parent exponential, \( a>0,a

eq1 \)) has no reflective symmetry (e.g., \( y = 2^{x} \) is increasing, not symmetric over y - axis or origin).

Answer:

B. Linear, D. Cubic, E. Rational/Reciprocal, F. Quadratic, G. Absolute Value