HA and VA
The end behavior of f(x) = (1/(x+2)) + 5.
What is limit as x approaches +/- infinity is 5?
How are holes created?
Dividing by a common factor.
When does a rational function have a slant asymptote?
When the degree in the numerator is exactly one more than the degree in the denominator.
f(x + 4) is what kind of translation in which direction from f(x)?
Left 4
Expand (x + 3y)^4
x^4 + 12x^3y + 54x^2y^2 + 108xy^3 + 81y^4
The horizontal asymptote of g(x) = (x+5)^2 / (x - 4).
No horizontal asymptote
How do you determine where the hole is?
Plug the x value into what remains after the function is reduced.
What is the slant asymptote of
f(x) = (x + 2)^2/(x + 2)
y = x + 2
g(3x) - 6 is what type of translation in which direction
horizontal dilation by a factor of 1/3,
vertical translation down 6
What is the third term of (2x - 3y)^9 or the coefficient of the x^7y^2 term?
9 C 2 (2x)^7 (-3y)^2
How do you determine vertical asymptotes?
Any remaining factors in the denominator that = 0 create V.A.
If you have a hole where there is a vertical asymptote what do you have?
Just a vertical asymptote.
y = (2x^2 - 6x + 7)/(x - 4) has a slant asymptote of
y = 2x + 2
4f(x - 5) describe the translations
vertical dilation by a factor of 4 and a horizontal shift right of 5
f(x) = { 0.2x^2 + 3x x<=0
{ 15 0< x<= 5
{ -x + 6 x > 5
What is f(3) and f(6)
f(3) = 15
f(6) = 0
VA of f(x) = (x^3 - 3x^2)/(x^2 + 8x + 15)
x = -5, x = - 3
f(x) = (x - 3)/(x^2 - 7x + 12) has a hole at x = 3.
Write the limit notation for the hole.
limit as x approaches 3 of f(x) = -1
If f(x) = (5x^2 + ax + 8)/(x + 2) has a slant asymptote of y = 5x - 6 what is a?
a = 4
-2 | 5 a 8
_____-10______
5 -6 a - 10 = - 6
a = 4
-(1/2)g(x) + 7
Reflection over the x axis, vertical dilation by a factor of 1/2 and a vertical shift up of 7
Price is inversely proportional to time cubed. If on the day 2 the price is $72 what is the price on day 4?
$9
Vertical asymptotes of f(x) = 1/(x^2 + 16)
None
f(x) = [(x - 5)(x+3)] / [(x - 5)^2 (x+3)]
Write the limit notation for the hole(s).
limit as x approaches - 3 of f(x) = - 1/8
y = (5x^2 + 4x - 9)/(2x + 1) has a slant asymptote of
y = 2.5x + 0.75
3(f(-(1/2)x)) + 9
Vertical dilation by factor of 3
reflection over the y axis
horizontal dilation by a factor of 2
vertical shift up 9
How do you determine if data is linear, quadratic, or cubic?
By finding the ....