For the Following Rational Function, Identify the Coordinates of All $$f ( x ) = \frac { 3 x ^ { 2 } - 4 x - 4 } { x - 2 }$$

question 106

Multiple Choice

For the following rational function, identify the coordinates of all removable discontinuities and sketch the graph. Identify all intercepts and find the equations of all asymptotes.
- $$f ( x ) = \frac { 3 x ^ { 2 } - 4 x - 4 } { x - 2 }$$

• A) removable discontinuity at \(( 2,8 )\); \(x\)-intercept: \(\left( - \frac { 2 } { 3 } , 0 \right) , y\)-intercept: \(( 0,2 ) ;\) no asymptotes
• B) removable discontinuity at \(( 2,0 )\); x-intercept: \(( 2,0 )\), y-intercept: \(( 0,2 )\); no asymptotes
• C) removable discontinuity at \(( 2 , - 4 )\); \(x\)-intercept: \(\left( \frac { 2 } { 3 } , 0 \right) , y\)-intercept: \(( 0,2 )\); no asymptotes
• D) removable discontinuity at \(( 2,4 )\); \(x\)-intercept: \(\left( \frac { 2 } { 3 } , 0 \right) , y\)-intercept: \(( 0,2 )\); \(x\)-intercept: \(( - 2,0 ) , y\)-intercept: \(( 0,2 )\); no asymptotes

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Definitions:

Demand Schedule

A demand schedule is a table that shows the quantity of a good or service that consumers are willing and able to purchase at various prices.

Price Elasticity

A measure of how much the quantity demanded of a good responds to a change in the price of that good.

Responsiveness of Quantity

The degree to which the quantity demanded or supplied responds to changes in price, income, or other factors.

Responsiveness of Price

The degree to which the demand or supply of a product changes in response to a change in price.