Question

Assuming there are no reflections or dilations, explain how you would write the equation of the function whose graph is sketched below.

Answer 1

Answer:

Start with the parent function y= 1/x^2

Add 3 to x in the denominator, because the graph is shifted left 3.

Add 1 to the fraction, because the graph is shifted up 1 unit.

Step-by-step explanation:

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Answer 2

The equation of the function shown in the provided graph is $y=\frac{1}{(x+3)^{2} }$.

The parent function is: $f(x)=\frac{1}{x^{2} }$

How horizontal shifting of the graph takes place?

If a function f(x) is shifted horizontally by k units the parent function f(x) becomes f(x+k) where k>0

Since the graph is shifted towards the negative x-axis by 3 units.

So, the parent function f(x) will become f(x+3).

$f(x)=\frac{1}{x^{2} }$

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

So, the equation of the function will be $y=\frac{1}{(x+3)^{2} }$.

Therefore, The equation of the function shown in the provided graph is $y=\frac{1}{(x+3)^{2} }$.

To get more about the graphs visit:

https://brainly.com/question/25020119