PLZZZ HELP ITS DUE VERY SOON! Write a function to represent each series of transformations:
• rotation of 90 degrees counterclockwise about the origin, point O, then a reflection across the x-axis
• reflection across the y-axis, then a translation a units to the right and b units up
• translation a units to the right and b units up, then a rotation of 180 degrees counterclockwise about the origin, then a reflection across the y-axis

Step-by-step explanation:

For the first one, I believe you would need to use a rotation matrix; to rotate 90º counterclockwise, the matrices would look like ; you would then multiply those out. A reflection across the x-axis would be changing the sign of f(x) (from negative to positive or positive to negative), a reflection across the y-axis would be changing the sign of x, translation a units to the right would be subtracting a from x, translation b units up would be adding b to x. Rotation of 180º about the origin would be the same format as the first matrix, except it would be cos180 and cos0 on the top and sin180 sin0 on the bottom. Reflection across the y-axis would be changing the sign of x again.

OR

1. We know that, 'Translation shifts the figure in any direction'.

As, the function f(x) is translated 'a' units to the right, the new form of function is f(x-a).

Again, the function is translated 'b' units up, the final form of the function is f(x-a)+b.

2 and 3. We know that, ' Reflection flips the image over a line'.

As the function g(x) is reflected over y-axis, the new form of the function is g(-x).

As the function h(x) is reflected over x-axis, the new form of the function is -h(x).

4 , 5 and 6. We know that, 'Rotation turns the image around a point to a certain degree'.

Let us assume the function to be a point (x,y).

As the function is rotated by 90° counterclockwise about the origin, the new function becomes ( y,-x ) i.e. R_{90}R

90

(x,y) = ( -y,x ).

As the function is rotated by 180° counterclockwise about the origin, the new function becomes ( y,-x ) i.e. R_{180}R

180

(x,y) = ( -x,-y ).

As the function is rotated by 2700° counterclockwise about the origin, the new function becomes ( y,-x ) i.e. R_{270}R

270

(x,

45

step-by-step explanation:

-7

step-by-step explanation:

x^2 + 18x + 74 = (x + 9)^2 - 81 + 74

= (x + 9)^2 - 7.

so q = -7.