Question

range for continuous relations
remember: ≤ \less than or equal to\
≥ \greater than or equal to\
1.
domain: ____________
range: ____________
function? _______, because...
circle graph
2.
domain: ____________
range: ____________
function? _______, because...
line graph

Explanation:

Problem 1 (Circle Graph)

Step1: Determine Domain (x - values)

Assume the circle is centered at the origin (0,0) with radius 3 (from grid). The leftmost x is -3, rightmost x is 3. So domain: $-3 \leq x \leq 3$.

Step2: Determine Range (y - values)

Bottommost y is -3, topmost y is 3. So range: $-3 \leq y \leq 3$.

Step3: Check if Function (Vertical Line Test)

A vertical line (e.g., x = 0) intersects the circle at two points (y = 3 and y = -3). So not a function.

Step1: Determine Domain (x - values)

The line is a straight line with no restrictions (extends infinitely left and right). So domain: All real numbers ($-\infty < x < \infty$ or $\mathbb{R}$).

Step2: Determine Range (y - values)

The line extends infinitely up and down. So range: All real numbers ($-\infty < y < \infty$ or $\mathbb{R}$).

Step3: Check if Function (Vertical Line Test)

Any vertical line intersects the line at exactly one point. So it is a function.

Answer:

Domain: $-3 \leq x \leq 3$
Range: $-3 \leq y \leq 3$
Function? No, because a vertical line intersects the graph at more than one point (fails Vertical Line Test).

Problem 2 (Line Graph)