Math  /  Algebra

QuestionWhat is the domain of the function? x>2x>-2 x>0x>0 x<2x<2 all real numbers

Studdy Solution

STEP 1

What is this asking? Which xx values make sense for this graph? Watch out! Don't mix up domain and range!
Domain is about the xx values, and range is about the yy values.

STEP 2

1. Look at the graph
2. Find the smallest xx
3. Find the largest xx
4. Write the domain

STEP 3

Alright, let's **carefully examine** this graph!
It's a curve that starts *just* to the right of the vertical line x=2x = -2 and keeps going to the right.

STEP 4

The curve seems to get *really* close to the line x=2x = -2, but it never *quite* touches it.
This means our smallest xx is a *teeny tiny* bit bigger than 2-2.

STEP 5

Now, look at the right side of the graph.
The curve keeps going and going to the right, forever!
That means there's no biggest xx value.
It just goes on to infinity!

STEP 6

So, we know the smallest xx is a bit bigger than 2-2, and there's no largest xx.
We can write this as x>2x > -2.
This means xx can be any number greater than 2-2.

STEP 7

The domain of the function is x>2x > -2.

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