Question

transformations of linear functions
name:
period (circle) 2a 3a 4a 1b 2b 4b
1
find ( g(x) ), where ( g(x) ) is the reflection across the ( x )-axis of ( f(x)=-9 x + 9 ).
write your answer in the form ( m x + b ), where ( m ) and ( b ) are integers.
( g(x)=)
2
find ( g(x) ), where ( g(x) ) is the reflection across the ( x )-axis of ( f(x)=-10 x + 7 ).
write your answer in the form ( m x + b ), where ( m ) and ( b ) are integers.
( g(x)=)
3
find ( g(x) ), where ( g(x) ) is the reflection across the ( y )-axis of ( f(x)=-3 x + 3 ).
write your answer in the form ( m x + b ), where ( m ) and ( b ) are integers.
( g(x)=)
4
find ( g(x) ), where ( g(x) ) is the reflection across the ( y )-axis of ( f(x)=-8 x + 7 ).
write your answer in the form ( m x + b ), where ( m ) and ( b ) are integers.
( g(x)=)

Explanation:

Step1: Reflection across the x - axis

For a function \(y = f(x)\), the reflection across the \(x\) - axis is \(y=-f(x)\). Given \(f(x)=-9x + 9\), then \(g(x)=-(-9x + 9)\).

Step2: Simplify the expression

Using the distributive property \(a(b + c)=ab+ac\) (here \(a=-1\), \(b=-9x\), \(c = 9\)), we have \(g(x)=9x-9\).

Step3: Another reflection across the x - axis

For \(f(x)=-10x + 7\), the reflection across the \(x\) - axis is \(g(x)=-(-10x + 7)\).

Step4: Simplify the second expression

Using the distributive property (\(a=-1\), \(b=-10x\), \(c = 7\)), we get \(g(x)=10x-7\).

Step5: Reflection across the y - axis

For a function \(y = f(x)\), the reflection across the \(y\) - axis is \(y = f(-x)\). Given \(f(x)=-3x + 3\), then \(g(x)=-3(-x)+3\).

Step6: Simplify the third expression

Using the distributive property (\(a=-3\), \(b=-x\)), we have \(g(x)=3x + 3\).

Step7: Reflection across the y - axis for the fourth function

Given \(f(x)=-8x + 7\), then \(g(x)=-8(-x)+7\).

Step8: Simplify the fourth expression

Using the distributive property (\(a=-8\), \(b=-x\)), we get \(g(x)=8x + 7\).

Answer:

1. \(g(x)=9x - 9\)
2. \(g(x)=10x - 7\)
3. \(g(x)=3x + 3\)
4. \(g(x)=8x + 7\)