How do you graph y=−2|5x+8|+4?

1 Answer
Sridhar V.
Mar 30, 2018

Please read the explanation.

Explanation:

Consider the General Form of the Absolute Value Function:

y=f(x)=a|bx−h|+k

a - responsible for Compressing/Stretching the graph.

b - When |b|>1, the graph of f(x)=|x| is compressed horizontally to produce the graph of y=|bx|.

It is interesting to note that the the sign of b does not affect the graph since the absolute value is considered.

h - responsible for Shifting the graph left/right.

k - responsible for Shifting the graph up/down.

The Parent Function is of the form y=f(x)=|x|

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The absolute value function y=−2|5x+8|+4 involve transformations.

Complete table of values for the graph:

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Analyze the behavior of the graph (in stages) of the given absolute value function:

(Images of graphs are in sequence to enable visual comprehension)

Graph 1 Graphs of y=|x|andy=|5x|

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Graph 2 Graphs of y=|x|andy=|5x+8|

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Graph 3 Graphs of y=|x|andy=−2|5x+8|

A negative value for a results in a reflection across the x-axis.

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Graph 4 Graphs of y=|x|andy=−2|5x+8|+4

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