Direct and Inverse Variation

Direct and Inverse Variation

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Warm-up......

Multiple Choice

What is the domain of  $\frac{6x+4}{\left(x-4\right)\left(x+5\right)}?$ 

•  $\left(-\infty,-5\right)\cup\left(-5,4\right)\cup\left(4,\infty\right)$  

•  $\left(-\infty,-4\right)\cup\left(-4,5\right)\cup\left(5,\infty\right)$ 

• x = -4 and x = 5 $\left(-\infty,-5\right)\cup\left(4,\infty\right)$  

•  $\left(-\infty,-1\right)\cup\left(-1,5\right)\cup\left(5,\infty\right)$  
  

Multiple Choice

 $g\left(x\right)\ =\ \frac{4x}{x-5}$  

What are the asymptotes?

• x = 5 & y = 4

• x = 5 & y = 0

• x = -5 & y = 4

• x = -5 & y = 0 

Multiple Choice

Simplify by cancelling

• 1

• -1

• Can't be simplified

Multiple Choice

Is the given table a direct or inverse variation? What is the constant of variation?

• Direct. k = 12

• Inverse. k = 12

• Direct. k = 1/12

• Inverse. k = 1/12

Multiple Choice

Is the given table a direct variation? If so, what is the constant of variation?

• Yes. k = 1/3

• Yes. k = 3

• Yes. k = 5

• No

Multiple Choice

Does x and y have a direct relationship?

• yes, because for every x there is a y

• yes, there is a common ratio of y to x which is 4

• no, the differences between x and y are not the same.

• it can not be determined.

Multiple Choice

Which of the given graphs is a direct variation?

• A

• B

• C

• D

Multiple Choice

Given y = 1.1x as the model for the maltese dogs example, about how long is a 10 year old maltese if he was 30 cm at 1 yr old?

• approximately 11.1 cm.

• approximately 44 cm

• approximately 33 cm.

• cannot be determined.

Multiple Choice

What is the formula for finding the constant of variation k for direct variation?

• k = xy

• $k\ =\ \frac{y}{x}$
  

Multiple Choice

If y varies directly to x, and y = 12 when x = 3, what is the equation that relates x and y?

• y=4x

• x=4y

• $y=\frac{4}{x}$

• none of these

Multiple Choice

If y varies directly to x, and y = 12 when x = 3, what is y when x = 5?

• x=5

• x=20

•  $y=\frac{4}{20}$ 

• none of these

Multiple Choice

What is the formula for k when it is an inverse variation?

• $k\ =\ \frac{y}{x}$
  

• $k\ =\ xy$

Multiple Choice

What is the formula in writing the equation when it is an inverse variation?

• $y=\frac{k}{x}$

• $y\ =\ kx$

Multiple Choice

y varies inversely with x, and y is 0.5 when x is 4. Which equation represents this situation?

• $y\ =\ 2x$
  

• $y\ =\ \frac{2}{x}$