Parent function:
[tex]y=\frac{1}{x^2}[/tex]
Transformations:
[tex]\begin{gathered} y=\frac{-a1}{(x\pm h)^2}\pm k \\ \\ -a:reflection\text{ }across\text{ }x-axis \\ +h:translation\text{ }h\text{ }units\text{ }to\text{ }the\text{ }left \\ -h:translation\text{ }h\text{ }units\text{ }to\text{ }the\text{ }right \\ +k:translation\text{ }k\text{ }units\text{ }up \\ -k:translation\text{ }k\text{ }units\text{ }down \end{gathered}[/tex]
To get function f:
[tex]f(x)=\frac{-1}{(x+1)^2}-3[/tex]To obtain the graph of f, shift (translated) graph of y to the left 1 unit, reflect across the x-axis and shift 3 units down.
Graph of y:
Graph of f; on the graph above use the transformations described above to get the graph of f(x):
y in blue
f(x) in green
For f:
a) domain: x-values for which it is defined, f is defined for all x except for x-1
Domain:[tex](-\infty,-1)\cup(-1,\infty)[/tex]
b) range: values taht takes the function, function takes values less than -3
Range:[tex](-\infty,-3)[/tex]
c) the function is increasing from -1 to infinite
[tex](-1,\infty)[/tex]
d) the function is decreasing from - infinite to -1:
[tex](-\infty,-1)[/tex]