Question

Assuming there are no reflections or dilations,
explain how you would write the equation of the
function whose graph is sketched below.
ty
4
-8
-4

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:

Answer 2

When a function is transformed, it means the function is either rotated, dilated, rotated or translated.

The equation of the function whose graph is sketched is:

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

The parent function is an inverse function of the form:

$y = \frac 1{x^2}$

The parent function is shifted in two ways.

1. 3 units left
2. 1 unit up

When a function is shifted to the left, the rule is:

$(x,y) \to (x + h,y)$

Where:

$h \to$ number of units.

So, we have:

$(x,y) \to (x + 3,y)$

The function becomes

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

When a function is shifted up, the rule is:

$(x,y) \to (x ,y+b)$

Where:

$b \to$ number of units.

So, we have:

$(x,y) \to (x ,y+1)$

The function becomes

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

So, the graph of the function in the given graph (see attachment) is:

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

Read more about transformations at:

https://brainly.com/question/11707700