which function transforms the graph of y= x^2 so that it is first shifted down 4 units and its then reflected across the y- axis?
A. y= -x^2 +4
B. y= -x^2 - 4
C. y= ( -x)^2 -4
D. y= - ( x + 4 )^2

If we have a function [tex]f(x) = ax ^ 2[/tex] and we want to transform it into a function g(x) that is equal to f(x) displaced c units down on the y-axis, then we must do:

[tex]g(x) = f(x) -c[/tex]

In this case we want to move the function 4 units down, then:

[tex]g(x) = f(x) -4\\\\g(x) = x ^ 2 -4[/tex]

Finally, to reflect the function on the y-axis. must do [tex]y = g(-x)[/tex]

Then we have the following function:

[tex]g(-x) = (-x) ^ 2 -4\\\\y = (-x) ^ 2 -4[/tex]

The answer is option C

javishajohnson02 javishajohnson02 · Answer 2 · 2020-11-30T14:32:26+01:00

javishajohnson02 javishajohnson02

30-11-2020

Answer:

The answer is c

Step-by-step explanation:

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which function transforms the graph of y= x^2 so that it is first shifted down 4 units and its then reflected across the y- axis? A. y= -x^2 +4 B. y= -x^2 - 4 C. y= ( -x)^2 -4 D. y= - ( x + 4 )^2

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which function transforms the graph of y= x^2 so that it is first shifted down 4 units and its then reflected across the y- axis?
A. y= -x^2 +4
B. y= -x^2 - 4
C. y= ( -x)^2 -4
D. y= - ( x + 4 )^2