College Algebra Lesson

​Chapter 3 Review

College Algebra (MATH 136)​

​Sections in Chapter 3...

​

• 3.1 Distance and Midpoint

• ​3.2 Functions and Graphs

• 3.3 Lines

• 3.4 Definition of a Function

• 3.5 Graphs of Functions

• 3.6 Quadratic Functions

• 3.7 Operations on Functions​

Multiple Choice

The graph shown corresponds with which equation?

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

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

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

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

Multiple Choice

What is the equation in STANDARD FORM of the line traveling through the points (2, -1) & (-4, 7)?

• $$y=-\frac{4}{3}x+\frac{5}{3}$$  

• $$y+1=2\left(x-3\right)$$  

• $$4x+3y=5$$  

• $$5x-3y=1$$  

Multiple Choice

Write the equation of the line perpendicular to $$y=-\frac{1}{3}x-7$$  that cuts through the point (1, -3) in slope-intercept form.

• $$y=\frac{1}{3}x-\frac{5}{3}$$  

• $$y=3x-6$$  

• $$y=3x-\frac{1}{3}$$  

• $$3x-y=5$$  

Multiple Select

Which of the following relations are FUNCTIONS? Select ALL that apply.

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

Multiple Choice

The Horizontal Line Test is used to determine if...

• a relation is a function.

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

• a function is constant.

Multiple Choice

What is the DOMAIN of the following function?

$$f\left(x\right)=\ \sqrt[]{-2x-7}$$  

• $$\left[0,\ \frac{7}{2}\right]$$  

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

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

• $$\left(-\infty,\ \infty\right)$$  

Multiple Choice

Select the correct set of transformations for $$f\left(x\right)=-\frac{1}{3}\ \sqrt[]{x+1}-2$$   from its parent, $$y=\ \sqrt[]{x}$$  .

• 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

Multiple Choice

If the green graph is $$f\left(x\right)$$  , what would be the equation for the transformed blue graph?

• $$y=f\left(x-2\right)$$  

• $$y=2f\left(x\right)$$  

• $$y=f\left(-x\right)$$  

• $$y=-f\left(x\right)$$  

Multiple Choice

What is the vertex of $$y=-x^2+2x+4$$  ?

• (-1/2, 3/2)

• (2, 7)

• (-1, 1)

• (1, 5)

Multiple Choice

Convert the quadratic function $$y=x^2-8x+3$$  into Vertex Form.

• $$y=\left(x-4\right)^2-19$$  

• $$y=\left(x+4\right)^2-13$$  

• $$y=\left(x-4\right)^2-13$$  

• $$y=\left(x+4\right)^2-19$$  

Multiple Choice

Find $$\left(f-g\right)\left(x\right)$$  .

$$f\left(x\right)=x+2$$  

$$g\left(x\right)=-2x^2+5x-1$$  

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

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

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

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

Fill in the Blanks

Find $\left(g\ o\ f\right)\left(-1\right)$  .

$f\left(x\right)=x^2+2$  

$g\left(x\right)=-3x+1$  

Multiple Choice

Find $$\left(f\ o\ g\right)\left(x\right)$$  .

$$f\left(x\right)=-2x^2-7$$  

$$g\left(x\right)=\ \sqrt[]{x-3}$$  

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

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

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

​That's it!

​

• ​This is a somewhat close simulation of the test!

• You can retry the practice version in Modules as much as you'd like!

• If something went poorly, address it soon!​