Question

Please match each function formula with the corresponding transformation of the parent function y= -x^2-1

Answer 1

Answer:

The answer in the attached figure

Step-by-step explanation:

we have the parent function

$y=-x^{2}-1$

case 1) Reflected across the x-axis

we know that

The rule of the transformation is

(x,y)------> (x,-y)

so

$y=-(-x^{2}-1)$

$y=x^{2}+1$

case 2) Reflected across the y-axis

we know that

The rule of the transformation is

(x,y)------> (-x,y)

so

$y=-(-x)^{2}-1$

$y=-x^{2}-1$

case 3) Translated left by 1 unit

we know that

The rule of the transformation is

(x,y)------> (x-1,y)

so

$y=-(x+1)^{2}-1$

case 4) Translated right by 1 unit

we know that

The rule of the transformation is

(x,y)------> (x+1,y)

so

$y=-(x-1)^{2}-1$

case 5) Translated down by 1 unit

we know that

The rule of the transformation is

(x,y)------> (x,y-1)

so

$y=-(x)^{2}-1-1$

$y=-(x)^{2}-2$

case 6) Translated up by 1 unit

we know that

The rule of the transformation is

(x,y)------> (x,y+1)

so

$y=-(x)^{2}-1+1$

$y=-(x)^{2}$