Question

a. domain:$3 leq x leq 5$
range:$y geqslant -2$
b. domain:$x geqslant -2$
range:$3 leq x leq 5$
c. domain: all real numbers
range:$y geqslant -2$
d. domain:$x geqslant -2$
range: all real numbers

Explanation:

Step1: Identify the domain

The graph is a parabola opening upwards, which extends infinitely left and right along the x-axis, so all real x-values are allowed.

Step2: Identify the range

The vertex of the parabola is at $y=-2$, and since it opens upwards, all y-values are greater than or equal to -2, so $y \geq -2$.

Answer:

c. Domain: All Real Numbers
Range: $y \geq -2$