What is f(x)=2x+1 equivalent to

Answer 1

Hello Kalsoom!

I hope this answer is helpful!

So, f(x) = 2x + 1 is a function which describes a straight line.

There are a couple of different ways of thinking about it.

First way,

If you are familiar with the y = mx + b formula, then we can simply notice that here m = 2 and b = 1.

So this is a line with slope 2, and y intercept 1.

Alternatively, if we calculate

f(0) = 2*0 + 1 = 0 + 1 = 1

then we know the point (0,1) is on the graph.

Then we could plot 2 more points by plugging in other values for x, and drawing a line through them would give us the graph of f(x) = 2*x + 1.

Second way,

When you say "what is f(x)=2x + 1 equivalent to", there are multiple different answers depending on what math class you are taking.

If you are in Algebra II, then perhaps you are asking about transformations.

Let's look at a function:

g(x) = x.

This is the simplest function, and is a simple line passing through the origin (0,0).

We can transform it to get f(x) = 2x + 1.

First, multiply by 2

so we get 2x.

This is the same as stretching the graph vertically by a factor of 2 (amplifying the graph).

So for example,

If you were looking at the point (1,1) on the graph, it gets stretched in the Y direction by a factor of 2.

So we get (1,2).

This is very easy to check.

If we plug in x = 1 into 2*x, we get 2*1 => 2.

So indeed, the point (1,1) has been transformed into (1,2).

Then if we add in 1 to get f(x), 2*x + 1, we end up shifting / moving the entire graph upwards vertically by 1.

So if you imagine a ruler laying on your desk, and you slide it upwards, while maintaining the same orientation, then this is the same kind of idea.

To imagine a given point again, we had (1,1) and we amplified the Y values by a factor of 2.

So we got (1,2)

then we shifted all the Y values up by 1.

So (1, 2 + 1) = (1,3).

So, 2x + 1 is equivalent to taking the graph of x, stretching it vertically by a factor of 2, and shifting it up by 1.

Third way of looking at it.

f(x) = 2x + 1 is equivalent to all the odd numbers, assuming your domain is the positive and negative integers.

Because if you enter in x = 0, 1, -1, 2, -2, ...

You get 1, 3, -1, 5, -3, 7, -5 ... which are all the odd numbers.

Does this answer your question? Please let me know if you need any more help, or if I didn't answer what you were asking! I hope this helped!