Intercepts
The y-intercept of the following function:
f(x) =
(x^2+6x -12)/(x^2 + 4x +6
What is... (0, -2)
The vertical asymptote of the function...
f(x) =
2/(x+4)
What is... x =-4
Factor: x2-12x+20
What is... (x-10)(x-2)
An equation that has a vertical asymptote at x = -4.
Note: Answers will vary
What is...
(x-3)/(x+4)
How do you identify the x-intercept?
Set y=0, solve for x then substitute x back into the equation to find the y value
The x-intercept(s) of the following function:
f(x) =
((x-3)(x+4))/((x+2)(x-1))
What is...
(3, 0) and (-4, 0)
The horizontal asymptote of the function:
f(x) =
(x^2-4x+3)/(2x^2-5x+6)
What is...y = 1/2
Factor: x2-49
What is...(x+7)(x-7)
An equation that has a horizontal asymptote at y=0
Note: Answers will vary
What is... Numerator Degree < Denominator degree
When comparing degrees of the numerator and the denominator, what is true about the degrees if the horizontal asymptote is
y=2/3
The degrees are the same. N=D
The x-intercept(s) of the following function...
f(x) =
(x^2-4)/(x^2+2x-3)
What is...(-2, 0) and (2, 0)
Identify the vertical asymptote of the function:
f(x)=
(x^2+x-12)/(x^2-9)
What is...x = -3
Factor...2x2-12x+16
What is...2(x-4)(x-2)
An equation that has a hole when x = -5
Note: Answers will vary
What is... equation must have a common factor in the numerator and denominator
Without graphing, how can you tell when a hole exists?
when there is a common factor in the numerator and the denominator
Identify the y-intercept of the following function:
f(x) =
((x - 2)(x -1))/((x+3)(x-4))
What is...(0, -1/12)
Identify the horizontal asymptote of the following function:
f(x) =
((5x-3)(2x+1))/((x-1)(3x+4))
What is... y = 10/3
Factor...2x2-32
What is...2(x+4)(x-4)
An equation that has a NO horizontal asymptote and a vertical asymptote at x = 2
What is...
y=((x-3)(x+6))/(4(x-2))
When is there NO horizontal asymptote?
When the degree of the numerator is greater than the degree of the denominator, N>D
The x-intercept(s) of the following function:
f(x) =
(x^3+x^2-20x)/(x^2-16)
What is...
(0, 0) and (-5, 0)
Identify the horizontal and vertical asymptote of the following function:
f(x) =
Horizontal Asymptote: y = 0
Vertical Asymptote: x=-5, 1
Factor: 9x2+90x-99
An equation that has a horizontal asymptote at y=3, has a vertical asymptote at x = -4, and a hole when x = 4.
What is...
y=(6x^2(x-4))/(2x(x^2-16)
Which asymptote can never be crossed?