Chapter 3 Review (College Algebra)

$$\left(x-3\right)^2+\left(y+1\right)^2=2$$  

$$\left(x-3\right)^2+\left(y-1\right)^2=4$$  

$$\left(x-3\right)^2+\left(y+1\right)^2=4$$  

$$\left(x+3\right)^2+\left(y+1\right)^2=2$$  

$$y=-\frac{4}{3}x+\frac{5}{3}$$  

$$y+1=2\left(x-3\right)$$  

$$4x+3y=5$$  

$$5x-3y=1$$  

$$y=\frac{1}{3}x-\frac{5}{3}$$  

$$y=3x-6$$  

$$y=3x-\frac{1}{3}$$  

$$3x-y=5$$  

$$\left\{\left(1,\ -2\right),\ \left(3,\ 4\right),\ \left(-10,\ 11\right)\right\}$$  

a relation is a function.

a function is one-to-one (injective).

a function is constant.

$$\left[0,\ \frac{7}{2}\right]$$  

$$\left[\frac{7}{2},\ \infty\right)$$  

$$\left(-\infty,\ -\frac{7}{2}\right]$$  

$$\left(-\infty,\ \infty\right)$$  

Shift left 1

Vertical reflection

Vertical shrink by 1/3

Shift down 2

Shift right 1

Vertical reflection

Vertical stretch by 3

Shift up 2

Shift right 1

Vertical reflection

Vertical shrink by 1/3

Shift up 2

Shift left 1

Vertical reflection

Vertical shrink by 1/3

Shift up 2

$$y=f\left(x-2\right)$$  

$$y=2f\left(x\right)$$  

$$y=f\left(-x\right)$$  

$$y=-f\left(x\right)$$  

(-1/2, 3/2)

(2, 7)

(-1, 1)

(1, 5)

$$y=\left(x-4\right)^2-19$$  

$$y=\left(x+4\right)^2-13$$  

$$y=\left(x-4\right)^2-13$$  

$$y=\left(x+4\right)^2-19$$  

$$\left(f-g\right)\left(x\right)=2x^2-4x+3$$  

$$\left(f-g\right)\left(x\right)=-2x^2-6x+3$$  

$$\left(f-g\right)\left(x\right)=2x^2+6x-1$$  

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

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

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

$$f\left(g\left(x\right)\right)=\ 2\ \sqrt[]{x-3}-1$$