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

1 Answer
Jan 27, 2018

Answer:

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]}