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

Answer:

(i)

$f(x)=-|x|$

(ii)

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

Step-by-step 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

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