Question

Which absolute value function, when graphed, represents the parent function, f(x) = |x|, reflected over the x-axis an Which absolute value function, when graphed, represents the parent function, f(x) = |x|, reflected over the x-axis and translated 1 unit to the right?d translated 1 unit to the right?

Answer 1

It is B

Explanation:

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Answer 2

(i)

`f(x)=-|x|`

(ii)

`f(x)=-|x-1|`

Explanation:

we are given two different questions

(i)

parent function is

`f(x)=|x|`

now, it is reflected over x-axis

Suppose, (x,y) is reflected over x-axis

(x,y) becomes (x,-y)

So, we replace y as -y and x remain same

so, we get

`-f(x)=|x|`

So, our required function is

`f(x)=-|x|`

(ii)

parent function is

`f(x)=|x|`

now, it is reflected over x-axis

Suppose, (x,y) is reflected over x-axis

(x,y) becomes (x,-y)

So, we replace y as -y and x remain same

so, we get

`-f(x)=|x|`

`f(x)=-|x|`

now, it is translated 1 unit to right side

Whenever any function is translated to right side by 'a' units

so, we can replace x as x-a

so, we can replace x as x-1 here

we get

`f(x)=-|x-1|`