Question

name
wednesday
which set of ordered pairs represents y as a function of x?
a {(0,0), (-1,2), (-1,-2), (-2,4), (-2,-4)}
b {(0,0), (1,1), (2,4), (3,9), (3,16)}
c {(0,0), (0,1), (0,2), (0,-1), (0,-2)}
d {(0,0), (-1,-0.5), (-2,-1), (-3,-1.5), (-4,-2)}
☐ parent signature
thursday
which graph represents y as a function of x?
a graph
c graph
b graph
d graph
☐ parent signature

Explanation:

Wednesday Question (Ordered Pairs as Function)

Step1: Recall Function Definition

A relation is a function if each \( x \)-value has exactly one \( y \)-value.

Step2: Analyze Option A

Set A: \( \{(0,0), (-1,2), (-1,-2), (-2,4), (-2,-4)\} \). Here, \( x = -1 \) has \( y = 2 \) and \( y = -2 \); \( x = -2 \) has \( y = 4 \) and \( y = -4 \). Not a function.

Step3: Analyze Option B

Set B: \( \{(0,0), (1,1), (2,4), (3,9), (3,16)\} \). \( x = 3 \) has \( y = 9 \) and \( y = 16 \). Not a function.

Step4: Analyze Option C

Set C: \( \{(0,0), (0,1), (0,2), (0,-1), (0,-2)\} \). \( x = 0 \) has multiple \( y \)-values. Not a function.

Step5: Analyze Option D

Set D: \( \{(0,0), (-1,-0.5), (-2,-1), (-3,-1.5), (-4,-2)\} \). Each \( x \)-value (\( 0, -1, -2, -3, -4 \)) has exactly one \( y \)-value. So it is a function.

Step1: Recall Vertical Line Test

A graph represents a function if no vertical line intersects the graph more than once.

Step2: Analyze Graph A

Graph A: A vertical line will intersect it at most once (appears to be a horizontal line? Wait, no, looking at the grid, it's a horizontal line? Wait, no, the first graph (A) – let's check vertical lines. For any \( x \), vertical line intersects once. Wait, no, maybe I missee. Wait, the options:

• Graph A: Let's assume it's a line (maybe horizontal? No, the arrows: maybe a horizontal line? Wait, no, the first graph (A) – when we apply vertical line test, any vertical line cuts it once.

• Graph B: A curve that's a "S" shape – vertical line will intersect twice (fails vertical line test).

• Graph C: A circle – vertical line through center will intersect twice (fails).

• Graph D: A vertical line (wait, no, Graph D is a vertical line? Wait, no, Graph D looks like a vertical line (x=2?); no, a vertical line has infinite y for one x – so fails vertical line test (since vertical line intersects it infinitely, but even one x with multiple y is enough). Wait, no: Graph D is a vertical line? No, the fourth graph (D) is a vertical line (two vertical lines? Wait, the image: Graph D has two vertical lines? No, maybe a single vertical line. Wait, no, the options:

Wait, the Thursday question:

• Graph A: Let's say it's a horizontal line (y=0? No, the arrows: maybe a horizontal line. Wait, no, the first graph (A) – when you draw a vertical line, it intersects once.

• Graph B: A curve that crosses a vertical line twice (so fails).

• Graph C: A circle – vertical line through x=0 (center) will intersect at (0,3) and (0,-3) – fails.

• Graph D: A vertical line (x=2? Or two vertical lines? No, a vertical line has x constant, so for x=2, multiple y – fails.

Wait, but the original marking: the student marked B? No, wait, the correct one is Graph A? Wait, no, let's recheck.

Wait, the vertical line test:

• Graph A: Passes (each vertical line intersects once).

• Graph B: Fails (vertical line intersects twice).

• Graph C: Fails (circle, vertical line intersects twice).

• Graph D: Fails (vertical line, so one x has multiple y).

So the correct graph is Graph A. Wait, but the student's marking: the image shows a mark on B? No, maybe I misinterpret. Wait, the options:

Wait, the first graph (A) – let's assume it's a horizontal line (y=0) – no, the arrows: maybe a horizontal line. Wait, no, the first graph (A) – when you apply vertical line test, any vertical line cuts it once. So Graph A passes.

Answer:

D. \( \{(0,0), (-1, -0.5), (-2, -1), (-3, -1.5), (-4, -2)\} \)

Thursday Question (Graph as Function)