Rational Functions - x&y intercepts & vertical asymptotes

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

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

•  $y=\frac{5}{2}$  

•  $y=\frac{5}{6}$  
  

•  $y=-5$  
  

•  $y=-3$