Question

Analyze the key features of the graph of f(x) shown below. Use rules of transformations and the parent function to formulate an equation for the rational function shown in the graph.

Answer 1

Answer:

The required equation is $f(x)=\frac{1}{x+3}-2$.

Step-by-step explanation:

The parent function of a rational function is

$g(x)=\frac{1}{x}$

The transformation is defined by the function

$f(x)=\frac{1}{x+a}+b$

Where, a represents the horizontal shift and b represents the vertical shift.

If a>0, then graph of parent function will shift left side and if a<0, then graph of parent function will shift right side.

If b>0, then graph of parent function will shift upward and if b<0, then graph of parent function will shift downward side.

Since the graph of parent function shifts 3 units left and 2 units down. Therefore the value of a is 3 and the value of b is -2.

The new function is

$f(x)=\frac{1}{x+3}-2$

Therefore the required equation is $f(x)=\frac{1}{x+3}-2$.