AnswersPrecalculusGraphing Rational Functions

Graphing Rational Functions — Quiz Answers

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1
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How does the graph of g of x is equal to the fraction with numerator 1 and denominator x minus 5 plus 2 compare to the graph of the parent function f of x is equal to 1 over x ?

A
g of x is shifted 5 units left and 2 units down from f of x .
B
g of x is shifted 5 units right and 2 units up from f of x .
C
g of x is shifted 5 units left and 2 units up from f of x .
D
g of x is shifted 5 units right and 2 units down from f of x .
2
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A function is shown. f⁡(x)=(3⁢x^2)/(4−8⁢x^2) The graph of f⁡(x) approaches a as x approaches infinity. What is a ? Enter your answer in the box.

Answer:

-3/8

3

What is the equation of the horizontal asymptote of the graph of y=(4⁢x^2−12)/(3⁢x^2+5⁢x+6) ? Enter your answer in the box.

Answer:

y=4/3

4

A certain company has a fixed cost of 200 dollars per day. It costs the company 3 point 1 0 dollars per unit to make its products. The company is tracking its average cost to make x units using f of x is equal to the fraction with numerator 200 plus 3 point 1 0 x and denominator x Which statement is true?

A
The horizontal asymptote of y is equal to 0 represents that the average cost per unit will approach 0 dollars as the number of units produced increases.
B
The vertical asymptote of x is equal to 3 point 1 0 represents that the average cost per unit will approach 3 point 1 0 dollars as the number of units produced increases.
C
The vertical asymptote of x is equal to 0 represents that the average cost per unit will approach 0 dollars as the number of units produced increases.
D
The horizontal asymptote of y is equal to 3 point 1 0 represents that the average cost per unit will approach 3 point 1 0 dollars as the number of units produced increases.
5

Which graph represents the function f of x is equal to 1 over x minus 1 ?

A
Image with description A coordinate plane with a graph showing two branches. The branch on the left approaches the x-axis as x approaches negative infinity from the right and approaches negative infinity as x approaches negative 1 from the left. Its turning point is near (negative 2 comma negative 1). The branch on the right approaches infinity as x approaches negative 1 from the right and approaches the x-axis as x approaches infinity from the left. Its turning point is near (0 comma 1).
B
Image with description A coordinate plane with a graph showing two branches. The branch on the left approaches y equals negative 1 as x approaches negative infinity from the right and approaches negative infinity as x approaches 0 from the left. Its turning point is near (negative 1 comma negative 2). The branch on the right approaches infinity as x approaches 0 from the right and approaches y equals negative 1 as x approaches infinity from the left. Its turning point is near (1 comma 0).
C
Image with description A coordinate plane with a graph showing two branches. The branch on the left approaches the x-axis as x approaches negative infinity from the right and approaches negative infinity as x approaches 1 from the left. Its turning point is near (0 comma negative 1). The branch on the right approaches infinity as x approaches 1 from the right and approaches the x-axis as x approaches infinity from the left. Its turning point is near (2 comma 1).
D
Image with description A coordinate plane with a graph showing two branches. The branch on the left approaches y equals 1 as x approaches negative infinity from the right and approaches negative infinity as x approaches 0 from the left. Its turning point is near (negative 1 comma 0). The branch on the right approaches infinity as x approaches 0 from the right and approaches y equals 1 as x approaches infinity from the left. Its turning point is near (1 comma 2).
6

What is the horizontal asymptote of f of x is equal to the fraction with numerator negative 2 x and denominator x plus 1 ?

A
y is equal to negative 2
B
y is equal to 1
C
y is equal to negative 1
D
y is equal to 0
7

What are the equations of the asymptotes of the graph of the function f of x is equal to the fraction with numerator 3 x squared minus 2 x minus 1 and denominator x squared plus 3 x minus 10 ?

A
x is equal to 3 , y is equal to negative 2 , and y is equal to 5
B
x is equal to 3 , y is equal to negative 5 , and y is equal to 2
C
x is equal to negative 2 , x is equal to 5 and y is equal to 3
D
x is equal to negative 5 , x is equal to 2 and y is equal to 3
8

What are the vertical and horizontal asymptotes for the function f of x is equal to the fraction with numerator 3 x squared and denominator x squared minus 4 ?

A
horizontal asymptote: y is equal to negative 4 , y is equal to 1 vertical asymptote: x is equal to 3
B
horizontal asymptote: y is equal to 3 vertical asymptote: x is equal to negative 4 , x is equal to 1
C
horizontal asymptote: y is equal to negative 2 , y is equal to 2 vertical asymptote: x is equal to 3
D
horizontal asymptote: y is equal to 3 vertical asymptote: x is equal to negative 2 , x is equal to 2
9

Which graph represents the function f of x is equal to the fraction with numerator 2 and denominator x minus 1 plus 4 ?

A
Image with description A coordinate plane with a graph showing two branches. The branch on the left approaches y equals negative 4 as x approaches negative infinity from the right and approaches negative infinity as x approaches 1 from the left. Its turning point is near (negative 1 comma negative 5). The branch on the right approaches infinity as x approaches 1 from the right and approaches y equals negative 4 as x approaches infinity from the left. Its turning point is near (2 comma negative 3).
B
Image with description A coordinate plane with a graph showing two branches. The branch on the left approaches y equals negative 4 as x approaches negative infinity from the right and approaches negative infinity as x approaches negative 1 from the left. Its turning point is near (negative 3 comma negative 5). The branch on the right approaches infinity as x approaches negative 1 from the right and approaches y equals negative 4 as x approaches infinity from the left. Its turning point is near (0 comma negative 2).
C
Image with description A coordinate plane with a graph showing two branches. The branch on the left approaches y equals 4 as x approaches negative infinity from the right and approaches negative infinity as x approaches negative 1 from the left. Its turning point is near (negative 3 comma 3). The branch on the right approaches infinity as x approaches negative 1 from the right and approaches y equals 4 as x approaches infinity from the left. Its turning point is near (0 comma negative 6).
D
Image with description A coordinate plane with a graph showing two branches. The branch on the left approaches y equals 4 as x approaches negative infinity from the right and approaches negative infinity as x approaches negative 1 from the left. Its turning point is near (negative 3 comma 3). The branch on the right approaches infinity as x approaches negative 1 from the right and approaches y equals 4 as x approaches infinity from the left. Its turning point is near (0 comma negative 6).
10

Which graph represents the function f of x is equal to the fraction with numerator 3 x minus 2 and denominator x minus 2 ?

A
Image with description A coordinate plane with a graph showing two branches. The branch on the left approaches y equals 2 and one-third as x approaches negative infinity from the right and approaches infinity as x approaches negative 2 from the left. Its turning point is near (negative 5 comma 5). The branch on the right approaches negative infinity as x approaches negative 2 from the right and approaches y equals 2 and one-third as x approaches infinity from the left. Its turning point is near (0 comma negative 1).
B
Image with description A coordinate plane with a graph showing two branches. The branch on the left approaches y equals 3 as x approaches negative infinity from the right and approaches negative infinity as x approaches 2 from the left. Its turning point is near (0 comma 1). The branch on the right approaches infinity as x approaches 2 from the right and approaches y equals 3 as x approaches infinity from the left. Its turning point is near (4 comma 5).
C
Image with description A coordinate plane with a graph showing two branches. The branch on the left approaches the x-axis as x approaches negative infinity from the right and approaches negative infinity as x approaches 2 from the left. Its turning point is near (1 comma negative 1). The branch on the right approaches infinity as x approaches 2 from the right and approaches the x-axis as x approaches infinity from the left. Its turning point is near (3 comma 1).
D
Image with description A coordinate plane with a graph showing two branches. The branch on the left approaches y equals one-third as x approaches negative infinity from the right and approaches infinity as x approaches 1 from the left. Its turning point is near (0 comma 1). The branch on the right approaches negative infinity as x approaches 1 from the right and approaches y equals one-third as x approaches infinity from the left. Its turning point is near (1 comma 0).

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