Question

Each statement describes a transformation of the graph of f(x) = x. Which statement correctly describes the graph of g(x) if g(x) = f(x) - 3?
A.
It is the graph of f(x) translated 3 units to the left.
B.
It is the graph of f(x) translated 3 units down.
C.
It is the graph of f(x) where the slope is decreased by 3.
D.
It is the graph of f(x) translated 3 units up.

Answer 1

Good morning @vannieduval. Welcome to Question Cove. How far did you get with attempting to solve this one? Mind sharing what you've done so far?

Answer 2

Well, I'm not entirely positive on what the answer is. To be honest I do not even know how to do this.

Answer 3

I see. So basically a function is just something that takes specific values as inputs and for each input only one output is generated. For graphing functions on an xy plane, we use the default equation y = f(x). This just means a function called f, will take x values as inputs also referred to as the domain and output a y value for each input also known as the range. Any questions about this so far?

Answer 4

So Y is output
X is input
F is function
Output = function(input)

Answer 5

That's a good summary of the information presented there. So in this case, f(x) = x, which is just the graph of y = x. Now, you're learning about transformations and just to keep it simple, let's say we have something like h(x) = x + a. The a variable would determine how many units the graph of f(x) moves vertically (up or down). If a is positive, then the graph of x will shift up vertically a units. If a is negative, then the graph will shift downward a units.

Answer 6

Okay.

Answer 7

We can write h(x) = f(x) + a to be consistent with what's above. All it means is that since f(x) = x, we just replace f(x) with x in the expression for h(x). Which is hopefully trivial for you to understand.

Answer 8

So given what I've just told you, what do you think is the difference between f(x) and g(x)?

Answer 9

Actually, before you answer that ...

Answer 10

Could you please re-write the equations for f(x) and g(x) here?

Answer 11

I'm afraid I am lost.

Answer 12

Would the answer be b? Because of the -3

Answer 13

Yes, the answer is b.

Answer 14

They wrote the equation with g(x) in a way that I think was meant to confuse you. Basically if we remove all the function stuff, you have

y = x
y = x - 3

Answer 15

And y = x - 3 is clearly a translation of y = x by 3 units south.

Answer 16

So basically, if you ever get confused, you can just remove the function stuff to see what you really have.

Answer 17

Okay, thank you. Could you help me with more?

Answer 18

If you want more help, you can close this question, then post a new one. And if you want my help for the next question, you can just tag me after posting the question.

Answer 19

Okay thanks :3