Rational Functions and Applications Quiz

Test your knowledge on rational functions: domains, asymptotes, degrees, holes, and behaviors. Get ready to ace your math quiz!

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

All real numbers except 2

All real numbers

Positive real numbers

All integers

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

x = -3, x = 2

x = -2, x = 3

x = -1, x = 6

x = 1, x = -6

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

x = -1, x = 3

x = -3, x = 1

x = -2, x = 3

x = -3, x = 2

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 = 2

x = 2, x = 3

x = 1, x = 3

x = 2, x = 4

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

Removable discontinuity

Vertical asymptote

Horizontal asymptote

Slant asymptote

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

x = 1

x = -1

x = 4

x = 2

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

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

y = 2x + 1

y = x + 2

y = 2x - 2

y = x - 1

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

x = -3/2

x = 3/2

x = -2/3

x = 2/3

#10

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

y = 5/3

y = 2/3

y = 1

y = -1

#11

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

x = 3

x = -3

x = 0

x = 9

#12

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

y = 2

y = -2

y = 0

There are no horizontal asymptotes

#13

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

x = 2

x = -2

x = 0

x = 4

#14

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

y = 3x - 1

y = 2x + 1

y = x - 2

There are no oblique asymptotes

#15

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

y = 2x - 1

y = 2x + 3

y = 2x - 3

y = 2x + 1

Rational Functions and Applications Quiz

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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