# Thread: How to identify whether it's a function, and visualizing how it looks?

1. ## How to identify whether it's a function, and visualizing how it looks?

Well today I received this question in class:

Identify each type of relation and predict whether it is a function. Then graph each function and use the vertical-line test to determine whether your prediction was correct.

a) y = 5 - 2x

b) y = 2x squared - 3

c) y = y = -3/4 (x + 3) squared + 1

d) x squared + y squared = 25

My question is, how will I know what type of function it is by just looking at the relations, and how would I imagine how each graph of one would look like? (Is there a rule I have to memorize?)

GR.11 Math (I forgot my GR.10 )

2. Functions have graphs that pass the Vertical Line Test: no vertical line will cross the graph more than once.

So do the graphs and look at the results.

Welcome to Math Help Forum!
Well today I received this question in class:

Identify each type of relation and predict whether it is a function. Then graph each function and use the vertical-line test to determine whether your prediction was correct.

a) y = 5 - 2x

b) y = 2x squared - 3

c) y = y = -3/4 (x + 3) squared + 1

d) x squared + y squared = 25

My question is, how will I know what type of function it is by just looking at the relations, and how would I imagine how each graph of one would look like? (Is there a rule I have to memorize?)

GR.11 Math (I forgot my GR.10 )
You will only be able to identify the type of relation if you're able to recognise the equation as being similar to something you know about, that you've seen before. So, of course, it depends on how much experience you've had at handling equations like these, and how good your memory is!

For instance, you may know that:

• $\displaystyle y = mx+c$ is a relation that produces a straight-line graph

• $\displaystyle y=ax^2+bx+c$ produces a symmetrical curve - in fact, a parabola - with a vertical axis of symmetry

• $\displaystyle x^2+y^2 = r^2$ describes a circle centre the origin radius $\displaystyle r$, since $\displaystyle x^2 + y^2$ is the square of the distance of the point $\displaystyle (x,y)$ from the origin.

You should now be able to make predictions about all four of the examples you've been given.