How do you graph y= 1/3 | x-3 | + 4?

1 Answer
Jan 27, 2018

graph{(1/3)abs(x-3)+4 [-3.865, 11.935, -0.68, 7.22]}

Explanation:

Let's start with the function y=x and describe the transformations taken in order to make the current function.

y=x
graph{y=x [-10, 10, -5, 5]}

First, we're taking the absolute value, meaning every negative y value is flipped across the x-axis and made positive.

y=abs(x)

graph{y=absx [-10,10,-5,5]}

Now, we have the function in terms of:

y=aabs(x-h)+k

where a=1/3, h=3, k=4. So let me explain what each of these means.

The parameter a is being multiplied by the x values, which determines the slope of the lines, which is the "rise"/"run" of the function, or (∆y)/(∆x). Since this is 1/3, we know that for every one increase in y, we get three increases in x.

y=1/3abs(x)
graph{1/3absx}

Next, the h value determines how far right we shift the function. NOTE: By default, the value is negative. If there is. a plus sign, you shift this function left.

Since this value is 3, we shift this three units right.

y=1/3abs(x-3)
graph{y=1/3abs(x-3)}

Finally, we have the lonely k value, which just tells us how far we shift this up. This value is four, and therefore we shift the graph 4 units up.

y=1/3abs(x-3)+4
graph{y=1/3abs(x-3)+4 [-3,11,-1,8]}