Transformations of Functions
What transformations are on the equation y=4x+2 if the parent function is x
Vertical dilation of 4 and vertical translation of up 2
{x+2 if, x>1
If f(x)={2 if, -1<=x<=1
{x-1 if, -3<x<-1
What is the value of f(x) at x=5
7
Hannah takes out a $1000 loan. She pays $250 every month. When does she pay it all off?
In 4 months
What is the parent function of 3x2+1
x2
What transformations have been applied to a function whose parent function is x
y-3=(x-2)
Up 3 and right 2
If f(x)={|x+4| x<-2
{-x+3 -2<=x<=2
{3x-6 x>2
What's the point at x=-5?
(-5,1)
What function is the best to model with for a sprinkler watering an area in a rotating motion?
Quadratic
What is the end behavior of x3 as x approaches negative infinity?
lim f(x)=-∞
x-->-∞
What transformations are on the function 1/4y=(3x)2+2 if the parent function is x2?
Vertical dilation of 4, horizontal dilation of 1/3, and vertical translation up 2.
{8x-5 if, x<-5
f(x)={-x-7 if, -5<=x<=7
{4x+6 if, x>7
What is f(-4)?
-3
If x^3 is the parent function what would the new function be if a horizontal dilation of 1/3 and a vertical translation up 2 be?
y=(3x)^3+2
At what point does f(x)=log(x) have an x intercept?
(1,0)
If the function 3x was dilated vertically by a factor of 5 and shifted to the left by 2 what would the point (3,9) turn into?
(1,45)
{0 if, x<0
f(x)={x if, 0<=x<1
{-x2-4x-2 if, 1<=x<3
{4-x if, x>3
What is f(2)?
-14
What would the function x^2 become after a vertical dilation of 2, a horizontal dilation of 1/5, a vertical translation up 8, and a horizontal translation right 4?
y=2(5(x-4))2+8
What is the limit as x approaches infinity of 1/x?
lim f(x)=0
x-->∞
-y=3(-4(x+2))2+2
What transformations are on the function if the parent function is x2?
Reflection over the y and x axis, vertical dilation of 3, horizontal dilation of 1/4, horizontal translation left 2, and vertical translation up 2.
{3x2-1 if, x<=-1
f(x)={ax+b if, -1<x<3
{2x+7 if, x>=3
What values of a and b would make the function have a domain of all real numbers?
a=2.75
b=4.75
Bacteria grow exponentially. At hour 3 the amount of bacteria is 10,000. At hour 5 the amount of bacteria is 40,000. Create a model for this scenario.
B(t)=1250(2)t
If ex has a horizontal asymptote at y=0 then what is the horizontal asymptote of y=-ex+2-5?
y=-5