Exam 6: Rational Expressions, Functions, and Equations

$Find the domain of the rational function. - f ( x ) = \frac { x ^ { 2 } - 81 } { x ^ { 2 } + 7 x - 18 }$ Find the domain of the rational function. - $f ( x ) = \frac { x ^ { 2 } - 81 } { x ^ { 2 } + 7 x - 18 }$

(Multiple Choice)

4.7/5

(38)

Question 61

Find the function value. - $f ( x ) = \frac { x + 6 } { 14 x - 13 } ; f ( - 2 )$

(Multiple Choice)

4.8/5

(36)

Question 62

Use the equation to solve the problem. $Use the equation to solve the problem. \text { Kurberof thures pasetsed } -Find and interpret f(40).$ $\text { Kurberof thures pasetsed }$ -Find and interpret f(40).

(Multiple Choice)

4.7/5

(34)

Question 63

Use the equation to solve the problem. $Use the equation to solve the problem. \text { Kurberof thures pasetsed } -What is the horizontal asymptote of the graph? What does this mean about the cost to produce x bobble-heads?$ $\text { Kurberof thures pasetsed }$ -What is the horizontal asymptote of the graph? What does this mean about the cost to produce x bobble-heads?

(Multiple Choice)

4.7/5

(28)

Question 64

Solve the problem. -A drug is injected into a patient and the concentration of the drug is monitored. The drug's concentration, $C ( t )$ , in milligrams after $t$ hours is modeled by $C ( t ) = \frac { 6 t } { 3 t ^ { 2 } + 2 }$ . Estimate the drug's concentration after 4 hours. (Round to the nearest hundredth.)

(Multiple Choice)

4.9/5

(50)

Question 65

Subtract. Simplify the result, if possible. - $\frac { x } { x ^ { 2 } - 16 } - \frac { 7 } { x ^ { 2 } + 5 x + 4 }$

(Multiple Choice)

4.9/5

(36)

Question 66

$\text { The rational function } f ( x ) = \frac { 120 x } { 100 - x } \text { models the cost, } f ( x ) \text {, in millions of dollars, to remove } x \% \text { of the trash from American }$ highways. The graph is shown. Use the equation to solve the problem. $\text { The rational function } f ( x ) = \frac { 120 x } { 100 - x } \text { models the cost, } f ( x ) \text {, in millions of dollars, to remove } x \% \text { of the trash from American } highways. The graph is shown. Use the equation to solve the problem. -Find and interpret f(80).$ -Find and interpret f(80).

(Multiple Choice)

4.8/5

(24)

Question 67

$Find the domain of the rational function. - f ( x ) = \frac { x ^ { 2 } - 9 } { x ^ { 2 } + 9 x + 14 }$ Find the domain of the rational function. - $f ( x ) = \frac { x ^ { 2 } - 9 } { x ^ { 2 } + 9 x + 14 }$

(Multiple Choice)

4.8/5

(38)

Question 68

Find the least common denominator of the rational expressions. - $\frac { x + 5 } { x ^ { 2 } - 5 x }$ and $\frac { - 10 } { x ^ { 2 } - 7 x + 10 }$

(Multiple Choice)

4.9/5

(36)

Question 69

Multiply as indicated. - $\frac { x ^ { 2 } - 7 x + 10 } { x ^ { 2 } - 21 x + 110 } \cdot \frac { x ^ { 2 } - 15 x + 44 } { x ^ { 2 } - 13 x + 40 }$

(Multiple Choice)

4.8/5

(30)

Question 70

Simplify the rational expression. If the rational expression cannot be simplified, so state. - $\frac { y ^ { 2 } + 6 y + 9 } { y ^ { 2 } + 9 y + 18 }$

(Multiple Choice)

4.9/5

(27)

Question 71

Multiply as indicated. - $\frac { x ^ { 2 } + 11 x + 28 } { x ^ { 2 } + 13 x + 42 } \cdot \frac { x ^ { 2 } + 11 x + 30 } { x ^ { 2 } + 9 x + 20 }$

(Multiple Choice)

4.8/5

(31)

Question 72

Divide as indicated. - $\frac { 21 x - 21 } { 11 } \div \frac { 7 x - 7 } { 66 }$

(Multiple Choice)

4.8/5

(39)

Question 73

$\text { The rational function } f ( x ) = \frac { 400 + 5 x } { x } \text { models the cost, } f ( x ) \text {, in dollars, to produce } x \text { bobble-head figures. The graph is show. }$ -According to the cost model, is it possible to remove 100% of the trash from American highways?

(Multiple Choice)

4.8/5

(35)

Question 74

$Find the domain of the rational function. - f ( x ) = \frac { x - 3 } { 6 }$ Find the domain of the rational function. - $f ( x ) = \frac { x - 3 } { 6 }$

(Multiple Choice)

4.8/5

(29)

Question 75

Find the least common denominator of the rational expressions. - $\frac { x - 1 } { x ^ { 2 } + 9 x + 8 }$ and $\frac { 1 } { x ^ { 2 } + x }$

(Multiple Choice)

4.9/5

(43)

Question 76

Simplify the rational expression. If the rational expression cannot be simplified, so state. - $\frac { 2 x ^ { 2 } - 18 x + 28 } { x - 7 }$

(Multiple Choice)

4.9/5

(31)

Question 77

Subtract. Simplify the result, if possible. - $\frac { 19 } { 22 x } - \frac { 6 } { 22 x }$

(Multiple Choice)

4.9/5

(32)

Question 78

Solve the problem. -Find the average of $\frac { 2 } { 5 }$ and $\frac { 5 } { 4 }$ (Hint: To find the average of two numbers, find their sum and divide by 2 .)

(Multiple Choice)

4.8/5

(37)

Question 79

Perform the indicated operations. Simplify the result, if possible. - $\frac { y - 3 } { y ^ { 2 } - 36 } + \frac { y - 3 } { 36 - y ^ { 2 } }$

(Multiple Choice)

4.9/5

(31)

Question 80

$Find the domain of the rational function. - f ( x ) = \frac { x ^ { 2 } - 81 } { x ^ { 2 } + 7 x - 18 }$ Find the domain of the rational function. - $f ( x ) = \frac { x ^ { 2 } - 81 } { x ^ { 2 } + 7 x - 18 }$

Find the function value. - $f ( x ) = \frac { x + 6 } { 14 x - 13 } ; f ( - 2 )$

Use the equation to solve the problem. $Use the equation to solve the problem. \text { Kurberof thures pasetsed } -Find and interpret f(40).$ $\text { Kurberof thures pasetsed }$ -Find and interpret f(40).

Subtract. Simplify the result, if possible. - $\frac { x } { x ^ { 2 } - 16 } - \frac { 7 } { x ^ { 2 } + 5 x + 4 }$

$Find the domain of the rational function. - f ( x ) = \frac { x ^ { 2 } - 9 } { x ^ { 2 } + 9 x + 14 }$ Find the domain of the rational function. - $f ( x ) = \frac { x ^ { 2 } - 9 } { x ^ { 2 } + 9 x + 14 }$

Find the least common denominator of the rational expressions. - $\frac { x + 5 } { x ^ { 2 } - 5 x }$ and $\frac { - 10 } { x ^ { 2 } - 7 x + 10 }$

Multiply as indicated. - $\frac { x ^ { 2 } - 7 x + 10 } { x ^ { 2 } - 21 x + 110 } \cdot \frac { x ^ { 2 } - 15 x + 44 } { x ^ { 2 } - 13 x + 40 }$

Simplify the rational expression. If the rational expression cannot be simplified, so state. - $\frac { y ^ { 2 } + 6 y + 9 } { y ^ { 2 } + 9 y + 18 }$

Multiply as indicated. - $\frac { x ^ { 2 } + 11 x + 28 } { x ^ { 2 } + 13 x + 42 } \cdot \frac { x ^ { 2 } + 11 x + 30 } { x ^ { 2 } + 9 x + 20 }$

Divide as indicated. - $\frac { 21 x - 21 } { 11 } \div \frac { 7 x - 7 } { 66 }$

$\text { The rational function } f ( x ) = \frac { 400 + 5 x } { x } \text { models the cost, } f ( x ) \text {, in dollars, to produce } x \text { bobble-head figures. The graph is show. }$ -According to the cost model, is it possible to remove 100% of the trash from American highways?

$Find the domain of the rational function. - f ( x ) = \frac { x - 3 } { 6 }$ Find the domain of the rational function. - $f ( x ) = \frac { x - 3 } { 6 }$

Find the least common denominator of the rational expressions. - $\frac { x - 1 } { x ^ { 2 } + 9 x + 8 }$ and $\frac { 1 } { x ^ { 2 } + x }$

Simplify the rational expression. If the rational expression cannot be simplified, so state. - $\frac { 2 x ^ { 2 } - 18 x + 28 } { x - 7 }$

Subtract. Simplify the result, if possible. - $\frac { 19 } { 22 x } - \frac { 6 } { 22 x }$

Solve the problem. -Find the average of $\frac { 2 } { 5 }$ and $\frac { 5 } { 4 }$ (Hint: To find the average of two numbers, find their sum and divide by 2 .)

Perform the indicated operations. Simplify the result, if possible. - $\frac { y - 3 } { y ^ { 2 } - 36 } + \frac { y - 3 } { 36 - y ^ { 2 } }$

Algebra, Mathematical Models, and Problem Solving

Functions and Linear Functions

Systems of Linear Equations

Inequalities and Problem Solving

Polynomials, Polynomial Functions, and Factoring

Radicals, Radical Functions, and Rational Exponents

Quadratic Equations and Functions

Filters

Exam 6: Rational Expressions, Functions, and Equations

Find the domain of the rational function. - f(x)=x2−81x2+7x−18f ( x ) = \frac { x ^ { 2 } - 81 } { x ^ { 2 } + 7 x - 18 }f(x)=x2+7x−18x2−81​

Find the function value. - f(x)=x+614x−13;f(−2)f ( x ) = \frac { x + 6 } { 14 x - 13 } ; f ( - 2 )f(x)=14x−13x+6​;f(−2)

Use the equation to solve the problem. Kurberof thures pasetsed \text { Kurberof thures pasetsed } Kurberof thures pasetsed -Find and interpret f(40).

Use the equation to solve the problem. Kurberof thures pasetsed \text { Kurberof thures pasetsed } Kurberof thures pasetsed -What is the horizontal asymptote of the graph? What does this mean about the cost to produce x bobble-heads?

Subtract. Simplify the result, if possible. - xx2−16−7x2+5x+4\frac { x } { x ^ { 2 } - 16 } - \frac { 7 } { x ^ { 2 } + 5 x + 4 }x2−16x​−x2+5x+47​

Find the domain of the rational function. - f(x)=x2−9x2+9x+14f ( x ) = \frac { x ^ { 2 } - 9 } { x ^ { 2 } + 9 x + 14 }f(x)=x2+9x+14x2−9​

Find the least common denominator of the rational expressions. - x+5x2−5x\frac { x + 5 } { x ^ { 2 } - 5 x }x2−5xx+5​ and −10x2−7x+10\frac { - 10 } { x ^ { 2 } - 7 x + 10 }x2−7x+10−10​

Multiply as indicated. - x2−7x+10x2−21x+110⋅x2−15x+44x2−13x+40\frac { x ^ { 2 } - 7 x + 10 } { x ^ { 2 } - 21 x + 110 } \cdot \frac { x ^ { 2 } - 15 x + 44 } { x ^ { 2 } - 13 x + 40 }x2−21x+110x2−7x+10​⋅x2−13x+40x2−15x+44​

Simplify the rational expression. If the rational expression cannot be simplified, so state. - y2+6y+9y2+9y+18\frac { y ^ { 2 } + 6 y + 9 } { y ^ { 2 } + 9 y + 18 }y2+9y+18y2+6y+9​

Multiply as indicated. - x2+11x+28x2+13x+42⋅x2+11x+30x2+9x+20\frac { x ^ { 2 } + 11 x + 28 } { x ^ { 2 } + 13 x + 42 } \cdot \frac { x ^ { 2 } + 11 x + 30 } { x ^ { 2 } + 9 x + 20 }x2+13x+42x2+11x+28​⋅x2+9x+20x2+11x+30​

Divide as indicated. - 21x−2111÷7x−766\frac { 21 x - 21 } { 11 } \div \frac { 7 x - 7 } { 66 }1121x−21​÷667x−7​

Find the domain of the rational function. - f(x)=x−36f ( x ) = \frac { x - 3 } { 6 }f(x)=6x−3​

Find the least common denominator of the rational expressions. - x−1x2+9x+8\frac { x - 1 } { x ^ { 2 } + 9 x + 8 }x2+9x+8x−1​ and 1x2+x\frac { 1 } { x ^ { 2 } + x }x2+x1​

Simplify the rational expression. If the rational expression cannot be simplified, so state. - 2x2−18x+28x−7\frac { 2 x ^ { 2 } - 18 x + 28 } { x - 7 }x−72x2−18x+28​

Subtract. Simplify the result, if possible. - 1922x−622x\frac { 19 } { 22 x } - \frac { 6 } { 22 x }22x19​−22x6​

Solve the problem. -Find the average of 25\frac { 2 } { 5 }52​ and 54\frac { 5 } { 4 }45​ (Hint: To find the average of two numbers, find their sum and divide by 2 .)

Perform the indicated operations. Simplify the result, if possible. - y−3y2−36+y−336−y2\frac { y - 3 } { y ^ { 2 } - 36 } + \frac { y - 3 } { 36 - y ^ { 2 } }y2−36y−3​+36−y2y−3​

Algebra, Mathematical Models, and Problem Solving

Functions and Linear Functions

Systems of Linear Equations

Inequalities and Problem Solving

Polynomials, Polynomial Functions, and Factoring

Radicals, Radical Functions, and Rational Exponents

Quadratic Equations and Functions

Filters

$Find the domain of the rational function. - f ( x ) = \frac { x ^ { 2 } - 81 } { x ^ { 2 } + 7 x - 18 }$ Find the domain of the rational function. - $f ( x ) = \frac { x ^ { 2 } - 81 } { x ^ { 2 } + 7 x - 18 }$

Find the function value. - $f ( x ) = \frac { x + 6 } { 14 x - 13 } ; f ( - 2 )$

Use the equation to solve the problem. $Use the equation to solve the problem. \text { Kurberof thures pasetsed } -Find and interpret f(40).$ $\text { Kurberof thures pasetsed }$ -Find and interpret f(40).

Subtract. Simplify the result, if possible. - $\frac { x } { x ^ { 2 } - 16 } - \frac { 7 } { x ^ { 2 } + 5 x + 4 }$

$Find the domain of the rational function. - f ( x ) = \frac { x ^ { 2 } - 9 } { x ^ { 2 } + 9 x + 14 }$ Find the domain of the rational function. - $f ( x ) = \frac { x ^ { 2 } - 9 } { x ^ { 2 } + 9 x + 14 }$

Find the least common denominator of the rational expressions. - $\frac { x + 5 } { x ^ { 2 } - 5 x }$ and $\frac { - 10 } { x ^ { 2 } - 7 x + 10 }$

Multiply as indicated. - $\frac { x ^ { 2 } - 7 x + 10 } { x ^ { 2 } - 21 x + 110 } \cdot \frac { x ^ { 2 } - 15 x + 44 } { x ^ { 2 } - 13 x + 40 }$

Simplify the rational expression. If the rational expression cannot be simplified, so state. - $\frac { y ^ { 2 } + 6 y + 9 } { y ^ { 2 } + 9 y + 18 }$

Multiply as indicated. - $\frac { x ^ { 2 } + 11 x + 28 } { x ^ { 2 } + 13 x + 42 } \cdot \frac { x ^ { 2 } + 11 x + 30 } { x ^ { 2 } + 9 x + 20 }$

Divide as indicated. - $\frac { 21 x - 21 } { 11 } \div \frac { 7 x - 7 } { 66 }$

$Find the domain of the rational function. - f ( x ) = \frac { x - 3 } { 6 }$ Find the domain of the rational function. - $f ( x ) = \frac { x - 3 } { 6 }$

Find the least common denominator of the rational expressions. - $\frac { x - 1 } { x ^ { 2 } + 9 x + 8 }$ and $\frac { 1 } { x ^ { 2 } + x }$

Simplify the rational expression. If the rational expression cannot be simplified, so state. - $\frac { 2 x ^ { 2 } - 18 x + 28 } { x - 7 }$

Subtract. Simplify the result, if possible. - $\frac { 19 } { 22 x } - \frac { 6 } { 22 x }$

Solve the problem. -Find the average of $\frac { 2 } { 5 }$ and $\frac { 5 } { 4 }$ (Hint: To find the average of two numbers, find their sum and divide by 2 .)

Perform the indicated operations. Simplify the result, if possible. - $\frac { y - 3 } { y ^ { 2 } - 36 } + \frac { y - 3 } { 36 - y ^ { 2 } }$