Math  /  Geometry

Question00 Eothth grade My|XI. Learning Ansesmart Asmalies: s
Which of these relations is a function? Video (1) Guemtiong answlored 117 Time elopered (D) 25 43 的 a smartsicore outortion 8 61 Submit Work it out Not feeling ready yet? These can help: Identry functions Lesson; Relations and finctions

Studdy Solution

STEP 1

What is this asking? Which of these graphs represents a function? Watch out! Remember, a function can only have *one* output for each input!

STEP 2

1. The Vertical Line Test
2. Apply the Test

STEP 3

A function is like a special machine: you put something in (xx), and it gives you *exactly one* thing out (yy).
If you put the same thing in twice, you should get the same thing out twice!

STEP 4

Imagine drawing vertical lines straight down through each graph.
If *any* vertical line touches the graph more than once, it's *not* a function!
Why? Because that means one input (xx value where the vertical line is) has multiple outputs (yy values where the line touches the graph).

STEP 5

A vertical line will only ever touch the V-shaped graph *once*.
This is a **function**!

STEP 6

Same story here!
Any vertical line will only intersect the parabola at a *single* point.
This is also a **function**!

STEP 7

Uh oh!
If we draw a vertical line through the *center* of the ellipse, it touches the graph *twice*!
This is *not* a function.

STEP 8

Just like the ellipse, vertical lines through the circle will touch it twice.
So, this is also *not* a function.

STEP 9

The top left (V-shaped graph) and the top right (parabola) represent functions.

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