What transformation transforms (p, q) to (q, p)?
a: a reflection over the x-axis
b: a reflection over the y-axis
c: a reflection over y = x
d: a rotation of 90° about the origin

Answer-

A reflection over the y=x, will transform (p, q) to (q, p)

Solution-

A reflection over the x-axis

When you reflect a point across the x-axis, the x-coordinate remains the same, but the y-coordinate is transformed into its opposite (sign is changed).

The point (x, y) becomes (x, -y)

A reflection over the y-axis

When you reflect a point across the y-axis, the y-coordinate remains the same, but the x-coordinate is transformed into its opposite (sign is changed).

The point (x, y) becomes (-x, y)

A reflection over y = x

When you reflect a point across the line y = x, the x-coordinate and y-coordinate change places (sign remains as it is).

The point (x, y) becomes (y, x)

A rotation of 90° about the origin

Rotation of point (x, y) about the origin O through 90° in clockwise direction, the new position will be (y, -x).

Rotation of point (x, y) about the origin O through 90° in counter-clockwise direction, the new position will be (-y, x).

Therefore, option C is correct.

let's add {f(x)=x+1}f(x)=x+1 and {g(x)=2x}g(x)=2x together to make a new function.

f(x)+g(x) =(x+1)+(2x)=x+1+2x=3x+1

let's call this new function hh. so we have:

{h(x)}={f(x)}+{g(x)}{=3x+1}h(x)=f(x)+g(x)=3x+1

we can also evaluate combined functions for particular inputs. let's evaluate function hh above for x=2x=2. below are two ways of doing this.

method 1: substitute x=2x=2 into the combined function hh.

h(x)

h(2)

​    

=3x+1

=3(2)+1

=7

​ since h(x)=f(x)+g(x)h(x)=f(x)+g(x), we can also find h(2)h(2) by finding f(2) +g(2)f(2)+g(2).

first, let's find f(2)f(2):

f(x)

f(2)

​    

=x+1

=2+1

=3

​  

now, let's find g(2)g(2):

g(x)

g(2)

​    

=2x

=2⋅2

=4

​  

so f(2)+g(2)=3+4=\greend7f(2)+g(2)=3+4=7.

notice that substituting x =2x=2 directly into function hh and finding f(2) + g(2)f(2)+g(2) gave us the same answer!