Question

How do you graph `y=-2abs(5x+8)+4`?

Answer 1

Please read the explanation.

Explanation:

Consider the General Form of the Absolute Value Function:

`color(red)(y=f(x) = a|bx-h|+k`

`color(red)(a` - responsible for Compressing/Stretching the graph.

`color(red)(b` - When `color(red)(|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.

`color(red)(h` - responsible for Shifting the graph left/right.

`color(red)(k` - responsible for Shifting the graph up/down.

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

The absolute value function `color(blue)(y=-2abs(5x+8)+4` involve transformations.

Complete table of values for the graph:

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 `color(blue)(y=|x| and y = |5x|`

Graph 2 Graphs of `color(blue)(y=|x| and y = |5x + 8|`

Graph 3 Graphs of `color(blue)(y=|x| and y = -2 |5x + 8|`

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

Graph 4 Graphs of `color(blue)(y=|x| and y = -2 |5x + 8| + 4`