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Rational Functions and Applications Quiz

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#1

What is the domain of the rational function f(x) = 1/(x - 2)?

All real numbers except 2
Explanation

Excluded point from the denominator

#2

If f(x) = (3x^2 + 2x - 5) / (x^2 + x - 6), what are the x-intercepts?

x = -2, x = 3
Explanation

Points where the function intersects the x-axis

#3

If f(x) = (2x^2 - 7x + 3) / (x^2 + 2x - 3), what are the vertical asymptotes?

x = -2, x = 3
Explanation

Vertical lines causing division by zero

#4

If f(x) = (3x^2 - 4x + 1) / (x^2 - 5x + 6), what are the x-values for the holes in the graph?

x = 1, x = 3
Explanation

Values causing removable discontinuity

#5

If f(x) = (2x^2 + x - 3) / (x^2 - 4), what is the behavior at x = 2?

Removable discontinuity
Explanation

Discontinuity at a point that can be canceled out by simplification

#6

Which of the following is the vertical asymptote of the rational function g(x) = (x^2 + 3x - 4) / (x - 1)?

x = 1
Explanation

Vertical line causing division by zero

#7

What is the degree of the numerator in the rational function h(x) = 2x^3 + 5x^2 - 3x + 1 / (x^2 - 1)?

3
Explanation

Highest power of x in the numerator

#8

What is the slant asymptote of the rational function g(x) = (2x^2 + 3x - 4) / (x - 1)?

y = 2x + 1
Explanation

The non-horizontal linear asymptote

#9

For the rational function h(x) = (4x^3 + 2x^2 + 7) / (2x^2 + 3), what is the vertical asymptote?

x = -3/2
Explanation

Vertical line causing division by zero

#10

What is the horizontal asymptote of the rational function g(x) = (5x^2 + 2x - 4) / (3x^2 - 1)?

y = 5/3
Explanation

Horizontal line representing the limiting behavior of the function

#11

If the rational function k(x) = (x^2 - 9) / (x + 3) is simplified, what is the hole in the graph?

x = -3
Explanation

Cancelled factor causing a hole

#12

For the rational function p(x) = (2x^2 - 5x + 3) / (x^2 - 4), what are the horizontal asymptotes?

There are no horizontal asymptotes
Explanation

Absence of limiting behavior as x approaches infinity

#13

If the rational function k(x) = (x^2 - 4) / (x - 2) is simplified, what is the removable discontinuity?

x = 2
Explanation

Point where the function is undefined but removable by cancellation

#14

For the rational function p(x) = (3x^2 + 2x + 1) / (x^2 - 1), what are the oblique asymptotes?

y = 2x + 1
Explanation

Non-horizontal linear asymptote

#15

If the rational function k(x) = (2x^2 - 9) / (x + 3) is simplified, what is the slant asymptote?

y = 2x - 1
Explanation

Non-horizontal linear asymptote

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