Rational Functions - x&y intercepts & vertical asymptotes

Presentation

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Mathematics

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9th - 12th Grade

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Practice Problem

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Medium

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CCSS

HSF-IF.C.7D

Standards-aligned

Michelle Rucker

Used 133+ times

FREE Resource

4 Slides • 10 Questions

Rational Functions - X & Y- intercepts & Vertical Asymptotes

f\left(x\right)=\frac{p\left(x\right)}{q\left(x\right)}

Multiple Choice

What is a rational function?

f\left(x\right)=\frac{p\left(x\right)}{q\left(x\right)}

A function where x has a rational exponent

A ratio of 2 functions

A quadratic function

A function that is easy to solve

Vertical Asymptotes

Vertical asymptotes are values of x, that the function never reaches. Since the denominator of a fraction cannot equal 0 (because it would make the value undefined), a rational function is undefined at any value of x that makes its denominator equal zero. To find the vertical asymptote of a rational function, set the denominator equal to zero and solve for x. .

Multiple Choice

Identify the vertical asymptote(s) of

f\left(x\right)=\frac{\left(x+3\right)\left(x-4\right)}{\left(x+1\right)\left(x-5\right)}

x=-3 and x=4

x=3 and x-4

x=1 and x=5

x=-1 and x=5

Multiple Choice

Identify the vertical asymptote(s) of

f\left(x\right)=\frac{5x}{x+6}

x=-6 and x=0

x=-6

x=5

x=-5 and x=0

Multiple Choice

Identify the vertical asymptote(s) of

f\left(x\right)=\frac{\left(x+7\right)\left(x-3\right)}{\left(x-6\right)\left(x+2\right)}

x=-7 and x=3

x=6 and x = -2

x=-6

x=2

X-intercepts

X-intercepts, also called "zeros", are the values of x where the function equals zero. If the numerator of the rational function equals zero, then the entire function equals zero. To find the x-intercept of a rational function, set the numerator equal to zero, and solve for x.

Multiple Choice

Identify the x-intercept(s) of:

f\left(x\right)=\frac{\left(x+3\right)\left(x-7\right)}{\left(x+1\right)\left(x+5\right)}

x=-1 and x=-5

x=-3 and x=7

x=1 and x = 5

x=3 and x=-7

Multiple Choice

Identify the x-intercept(s) of:

f\left(x\right)=\frac{x+2}{\left(x+1\right)\left(x+5\right)}

x=-1 and x=-5

x=2

x=-2

x=1 and x=5

Multiple Choice

Identify the x-intercept(s) of:

f\left(x\right)=\frac{x+5}{x^2-4x+2}

x=-5

x=5

x=-2

x=4

Y-intercepts

The y-intercept of a function (the point at which is crosses the y-axis) can be found by replacing x with zero, and then solving for y. To find the y-intercept of a rational function, replace every x with zero and evaluate what remains.

Multiple Choice

Identify the y-intercept(s) of

$f\left(x\right)=\frac{\left(x+4\right)\left(x+1\right)}{\left(x+3\right)\left(x+3\right)}$

$y=-4$

$y=\frac{5}{6}$

$y=-1$

$y=\frac{4}{9}$

Multiple Choice

Identify the y-intercept(s) of

$f\left(x\right)=\frac{x^2-9}{x^2-8x+7}$

$y=9$

$y=-\frac{9}{7}$

$y=-8$

$y=\frac{4}{9}$

Multiple Choice

Identify the y-intercept(s) of

$f\left(x\right)=\frac{x+5}{x^2+3x+2}$

$y=\frac{5}{2}$

$y=\frac{5}{6}$

$y=-5$

$y=-3$

Rational Functions - X & Y- intercepts & Vertical Asymptotes

f\left(x\right)=\frac{p\left(x\right)}{q\left(x\right)}

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