Question

which parent functions have negative y-values?
□ absolute value
□ linear
□ greatest integer
□ cubic
□ exponential
□ rational
□ square root
□ quadratic

Explanation:

1. Absolute Value: The parent absolute value function is \( y = |x| \), which has \( y\geq0 \) for all \( x \), so it does not have negative \( y \)-values.
2. Linear: The parent linear function is \( y = x \). When \( x<0 \), \( y<0 \), so it can have negative \( y \)-values.
3. Greatest Integer: The parent greatest integer function (floor function) \( y=\lfloor x

floor \). For example, when \( x = - 0.5 \), \( y=-1 \), so it can have negative \( y \)-values.

1. Cubic: The parent cubic function is \( y = x^{3} \). When \( x<0 \), \( x^{3}<0 \) (e.g., \( x=-1 \), \( y = - 1 \)), so it can have negative \( y \)-values.
2. Exponential: The parent exponential function is \( y = a^{x}\) (\(a>0,a

eq1\)). Since \( a^{x}>0 \) for all real \( x \), it does not have negative \( y \)-values.

1. Rational: The parent rational function (e.g., \( y=\frac{1}{x} \)) has negative \( y \)-values when \( x<0 \) (e.g., \( x = - 1 \), \( y=-1 \)), so it can have negative \( y \)-values.
2. Square Root: The parent square root function is \( y=\sqrt{x} \), with domain \( x\geq0 \) and \( y\geq0 \), so it does not have negative \( y \)-values.
3. Quadratic: The parent quadratic function is \( y = x^{2}\), with \( y\geq0 \) for all \( x \), so it does not have negative \( y \)-values.

Answer:

B. Linear, C. Greatest Integer, D. Cubic, F. Rational