Vocab
What do you equal to zero to get your vertical asymptote?
The denominator of the simplified expression
What is your Horizontal Asymptote
(3x^2+x)/(6x^3+11x^2+3x)
Y=0
What is the Horizontal Asymptote of the function
(6x^2+7x+2)/(9x^2-16)
y=2/3
What is the horizontal asymptote of
(2x^2+10x+12)/(3x^2+27x+42)
y=2/3
What is the parent function of a reciprocal function
1/x
What do you equal to zero to get your x-intercept?
The numerator of the simplified expression
What is the vertical asymptote
(3x^2+x)/(6x^3+11x^2+3x)
x=-1.5
What is the vertical asymptote
(6x^2+7x+2)/(9x^2-16)
x=-4/3 and x=4/3
What is the domain of the following function
(2x^2+10x+12)/(3x^2+27x+42)
All real numbers such that x does not equal -7 and -2
3/(2x^2)=5/(4x^2)-2/(x)
x=-1/8
Take the standard form of a reciprocal. What movement does the H cause.
Extra points: What does a negative h do what does a positive h do
(a)/(x-h)+k
Horizontal shift/translation
Extra: Negative h moves right
Positive h moves left
What do you look at to get your horizontal asymptote?
The degree(power) of the numerator and denominator
What is the x-intercept(s) of the function
(3x^2+x)/(6x^3+11x^2+3x)
None
What is the x-intercept
(6x^2+7x+2)/(9x^2-16)
(-2/3,0) and (-1/2,0)
What is the x-intercepts
(2x^2+10x+12)/(3x^2+27x+42)
(-3,0)
(2x)/(x-5)=7/(x-5)
x=7/2
Take the standard form of a reciprocal. What movement does the k cause.
Extra points: What does a negative k do what does a positive k do
(a)/(x-h)+k
Vertical Shift
-Down
+Up
What do you equal to zero to get the hole of the function
What you crossed out equal to zero for your x-value and for your y-value you get your x-value and plug it in to your simplified expression
What is the domain of the function
(3x^2+x)/(6x^3+11x^2+3x)
All real numbers such that x does not equal x={-1.5, -1/3, 0}
What is the y-intercept of the function
(6x^2+7x+2)/(9x^2-16)
y=-1/8
What is the y-intercept
(2x^2+10x+12)/(3x^2+27x+42)
(0,2/7)
Solve the following
3/(2x^2)=5/(4x^2)-2x
x=-1/2
Take the standard form of a reciprocal. What movement does the a cause.
Extra points: What does a negative a do
(a)/(x-h)+k
Less than 1 and bigger than zero (decimal/fraction) Compression
Greater than 1 Stretch
Negative a is a reflection across the x-axis
How do you get your y-intercept
Put a zero for all your x-values of the simplified expression then simplify. What is left over is your y-intercept.
What is the hole of the function
(3x^2+x)/(6x^3+11x^2+3x)
x=-1/3 and x=0
What is the hole of the function
(6x^2+7x+2)/(9x^2-16)
None
What is the hole
(2x^2+10x+12)/(3x^3+27x+42)
(-2,2/15)
2/(x-5)-1=7/(x-5)
Describe the transformations that occurred to f(x)=1/x when changed to
g(x)=-3/(x-2)-4
Reflected across the x-axis
Stretch by 3
Right by 2
Down by 4