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Question

Which is the equation of the function?

f(x) = 3|x| + 1

f(x) = 3|x – 1|

f(x) = |x| + 1

f(x) = |x – 1|

Answer 1

Notice that the slopes of the line segments are (-1/3) and (1/3).

The x values are 'shifted' so that the point (1,0) is the intersection of the two segments.

The equation of the function is: f(x) = (1/3)|x-1|

Answer 2

Hi,

There are two ways to solve this question. The first way is to use brute force, and this may take longer. You can plug in x values ranging from -4 to 4 into all the given equations and see which ones give you the correct output or y values.

The faster way is to remember how f(x) = |x| looks like. So, the vertex for |x| is always at the origin (0,0), and if do something like |x-1|, this shifts the graph right one place from the origin (0,0). This means that the graph |x-1| is now located at the point (1,0).

If I do something like |x+1|, this shifts the graph one place to the left from the origin (0,0). That means the graph is at (-1,0) now.

Ok, so now let's talk about what a whole number (3) or a fraction (1/5) does to the graph |x|.

When I have something like (whole number * |x|) this makes the graph narrower. Whereas when I have something like (fraction * |x|) this makes the graph wider.

For a visual demonstration, please visit Desmos and type in either a fraction or a whole number with an absolute value function.

https://www.desmos.com/calculator

Now that we have a better understanding of what the absolute value graphs would look like let's work on the question above.

# By how much is the graph moving? Well, it seems like the graph moved 1 place to the right from the original graph |x|. So it must have something like this |x-1|.

# Is the graph narrower or wider? It looks like the graph is wider, so there must be a fraction. The only answer that matches our graphic is f(x) = 1/3 * |x-1| thus, that is our answer.

I hope this helps, and please reach out if you need more help!

Answer 3

We know that the graph is shifted to the right by 1 unit so

we can start off with f(x) = |x – 1|

Since the graph is stretched, we know that a value in y = a|x|

has to be less than 1.

So the answer is f(x) = |x – 1|