4.1-4.3 Review

4.1-4.3 Review

4.1 Direct and Inverse Variation

• Direct Variation - Multiply

• Inverse Variation - Divide

• Joint Variation - Multiply (many variables)

Multiple Choice

What kind of variation does this equation show?
y = 6x

• Inverse Variation
• Direct Variation
• No Variation
• Joint Variation

Multiple Choice

What kind of variation is shown in the graph?

• Direct
• Inverse

Multiple Choice

What kind of variation is shown in this graph?

• Inverse
• Direct

Multiple Choice

Does the table show an inverse variation?

• Yes
• No

Multiple Choice

Given that y varies inversely with x, if x =7 and y = 4, what is y when x = 2?

• 14

• 10

• 2

• -14

4.2 Graphing Rational Functions

• Vertical Asymptotes- Denominator =0

• Horizontal Asymptotes- Cases

Multiple Choice

Find the vertical asymptote.

x²-2x-8

__________

3x-2

• y=2/3

• x=3/2

• x= 2/3

• x=1/3

Multiple Choice

What are the asymptotes?

• x = -3 y = 1

• x = 3 y = 1

• x = -3 y = -1

• x = 3 y = -1

Multiple Choice

What is the horizontal asymptote?

• x = 2

• x = 7

• y = 2

• y = 7

Multiple Choice

What is the Vertical Asymptote?

• x= -5

• x= 5

• x= 6

• x= -6

Multiple Choice

What is the horizontal asymptote of this function?

• y=2

• x=1/2

• y=1

• y=1/2

Multiple Choice

What is the horizontal asymptote?

• y = -4

• y = 1

• x = 1

• y = -6

Multiple Choice

What is the horizontal asymptote to this function?

• y=4

• y=0

• y=-2

• y=1

Multiple Choice

How is this function transformed from the parent function?

• Translated left and up

• Translated right and up

• Translated left and down

• Translated right and down

4.3 Day 1: Simplify + Multiply Rational Functions

• To Simplify - FACTOR then divide

• To Multiply- FACTOR then divide

• To Divide- Multiply by the reciprocal (Keep, Change, Flip), FACTOR, then divide

Multiple Choice

What are the restricted values?

• x = - 3 and x = 4

• x = 3 and x = - 4

• x = 3 only

• x = - 4 only

Multiple Choice

What is the domain?

• x ≠ 3

• x ≠ -1

• x ≠ 3, -1

• x ≠ 3, 1

Multiple Choice

Simplify the rational function

• 1/(x + 5)

• 1/(x - 5)

• (x - 5)(x + 5)

• (x - 5)/[(x - 5)(x + 5)]

Multiple Choice

Simplify.

• $\frac{a-4}{a-4}$

• $\frac{2\left(a-4\right)}{\left(a+4\right)\left(a-4\right)}$

• $\frac{a-4}{a+4}$

• 1

Multiple Choice

Multiply

• A.

• B.

• C.

• D.

Multiple Choice

Divide the rational expression below.

• $\frac{x+10}{2x+5}$

• $\frac{2}{5x-1}$

• $\frac{12}{x+10}$

• $\frac{2x+5}{x+10}$

Multiple Choice

The holes of a rational function occur when :

• my pencil pokes a hole in the paper I'm working on
• there is something left in the denominator
• the value of f(0)
• a factor in the denominator cancels with a factor in the numerator

Multiple Select

 $f\left(x\right)=\frac{\left(x+7\right)\left(x-3\right)\left(x+1\right)}{\left(x-3\right)\left(x-5\right)}$  

Select all of the true statements.

• A hole occurs where x=3

• vertical asymptote at x=3

• vertical asymptote at x=5

• A hole occurs where x=5

Multiple Choice

What is the hole? $g\left(x\right)=\frac{\left(x-2\right)\left(x+10\right)}{\left(x+2\right)\left(x-2\right)}$  

• (2, 3)

• (2,0)

• (-2,10)

• (2, 10)

Multiple Choice

Does this function have any vertical asymptotes? If so, what are their equations? $y=\frac{\left(x+3\right)\left(x-4\right)\left(x+7\right)}{\left(x-4\right)}$   

• No vertical asymptotes.

• One vertical asymptote: x = 4

• Two vertical asymptotes: x = -3 and x = -7

• Three vertical asymptotes:  x = -3, x = 4, and x = -7

Multiple Choice

Find the vertical asymptotes and holes of the function.

• Holes: None;

  VA: x = 1, -3

• Holes: (-3, 1/-4);

  VA: x = 1

• Holes: (-3,0),(1,0)

  VA: None

• Holes: (1,1)

  VA: x = -3

Multiple Choice

What is the hole?

• (4,5)

• (-4,0)

• (5, 10/9)

• (-5, 0)

Multiple Choice

What is the VA?

• x= 4

• x= -4

• x= 5

• x= -5