For the Following Rational Function, Identify the Coordinates of All $$f ( x ) = \frac { x - 4 } { x ^ { 2 } - 7 x + 12 }$$

question 23

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.
- $$f ( x ) = \frac { x - 4 } { x ^ { 2 } - 7 x + 12 }$$

• A) no removable discontinuities; no \(\mathrm { x }\)-intercept, no \(\mathrm { y }\)-intercept asymptotes \(x = 3 , x = 4 , y = 0\)
• B) no removable discontinuities; no \(\mathrm { x }\)-intercept, no \(\mathrm { y ; no \(x\)-intercept, no \(y\)-intercept; asymptotes \(x = - 3 , x = - 4 , y = 0\)
• C) removable discontinuity at \(( - 4 , - 1 )\); no \(x\)-intercept, \(y\)-intercept: \(\left( 0 , \frac { 1 } { 3 } \right)\); asymptotes \(x = - 3 , y = 0\)
• D) removable discontinuity at \(( 4,1 )\); no \(x\)-intercept, \(y\)-intercept: \(\left( 0 , - \frac { 1 } { 3 } \right)\) asymptotes \(x = 3 , y = 0\)

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Definitions:

Absorption Costing Income Statement

An income statement format that incorporates the full cost of manufacturing a product, including both fixed and variable manufacturing costs, in determining the cost of goods sold.

Gross Profit

The difference between revenue and the cost of goods sold, indicating the efficiency of a company in managing its labor and supplies in the production process.

Cost of Goods Sold

Costs directly linked to the manufacture of goods a company sells, encompassing both materials and labor expenses.

Variable Selling

Costs that fluctuate in direct proportion to changes in sales volume, such as commissions and shipping charges.