Unit 1B Review (Algebra 2)

Shift left 5, down 3

Shift left 3, down 5

Shift right 5, up 3

Shift right 3, down 5

Vertical shrink by 1/3, shift right 4

Vertical stretch by 3, shift left 4

Vertical stretch by 3, shift right 4

Vertical shrink by 1/3, shift left 4

$$f\left(x\right)=\left|x-2\right|+1$$  

$$f\left(x\right)\left|x-1\right|+2$$  

$$f\left(x\right)=\left|x+1\right|+2$$  

$$f\left(x\right)=\left|x+2\right|-1$$  

$$f\left(x\right)=\frac{1}{3}\left|x-7\right|$$  

$$f\left(x\right)=\frac{1}{3}\left|x\right|-7$$  

$$f\left(x\right)=3\left|x+7\right|$$  

$$f\left(x\right)=3\left|x\right|-7$$  

$$\left\{\left(0,1\right),\ \left(-4,\ -3\right),\ \left(10,-5\right)\right\}$$  

$$\left\{\left(1,0\right),\ \left(-3,\ -4\right),\ \left(-5,\ 10\right)\right\}$$  

$$\left\{\left(0,-1\right),\ \left(4,3\right),\ \left(-10,5\right)\right\}$$  

rotated

reflected

translated

dilated

$$f^{-1}\left(x\right)=-\frac{1}{2}x-3$$  

$$f^{-1}\left(x\right)=2x-6$$  

$$f^{-1}\left(x\right)=\frac{1}{2}y-3$$  

$$f^{-1}\left(x\right)=2x+3$$  

$$\left(f-g\right)\left(x\right)=4x+2$$  

$$\left(f-g\right)\left(x\right)=2x-6$$  

$$\left(f-g\right)\left(x\right)=-2x+6$$  

$$\left(f-g\right)\left(x\right)=x-4$$  

$$\left(f\cdot g\right)\left(x\right)=3x^2+10x-8$$  

  $$\left(f\cdot g\right)\left(x\right)=x^2-7x+10$$  

$$\left(f\cdot g\right)\left(x\right)=3x^2+14x+8$$  

$$\left(f\cdot g\right)\left(x\right)=-2x^2-7x+1$$  

$$\left(g\ ∘\ f\right)\left(x\right)=-7x^2-5$$  

$$\left(g\ ∘\ f\right)\left(x\right)=3x^2-5$$  

$$\left(g\ ∘\ f\right)\left(x\right)=49x^2-28x+6$$