The Basics
In the general formula, how does k transform the graph?
f(x)=asqrt(x-h)+k
+k goes up, -k goes down
What transformations are happening?
g(x)=-1/2sqrt(x+3)-7
Vertical compression by 1/2, left 3, down 7, reflection over the x-axis
Write the cube root function equation that has a vertical stretch by 3, right 6, and up 5
g(x)=3root(3)(x-6)+5
For any cube root function what is the domain and range?
All real numbers!!
Sally says the k = 3 in the given equation. Is she correct?
f(x)=2sqrt(x-4)+3
Yes Sally is correct! Go Sally!
In the general formula, how does h transform the graph?
f(x)=asqrt(x-h)+k
positive h makes it go right, negative h makes it go left.
Write the square root function equation for a horizontal stretch by 4, left 6, and up 5
f(x)= sqrt(1/4(x+6)) +5
What transformations are happening?
f(x)= root(3)(-1/3(x-4))-9
Horizontal stretch by 3, right 4, down 9, reflection over the y-axis
What is the domain and range of the following function?
g(x)=-2root(3)(x+4)+5
All real numbers!!
Sally says the h = -4 in the given equation. Is she correct?
f(x)=2sqrt(x-4)+3
No Sally made a mistake! h = 4 becuase the negative is part of the equation!
In the general formula, what does a do?
g(x)=aroot(3)(1/bx-h)+k
a makes a vertical stretch or compression, and a < 0 reflection over the x-axis
g(x)=-1/2sqrt(x+3)-7
What are the reference points for this square root function?
(0,0)-->(-3,-7)
(1,1)-->(-2,-7.5)
What are the reference points for this cubic functions?
g(x)=3root(3)(x-6)+5
(-1,-1)-->(5,2)
(0,0)-->(6,5)
(1,1)-->(7,8)
What is the domain of this function?
f(x)=2sqrt(x-3)-5
increasing function so
{x|x>=3}
{y|y>=-5}
Sally says the the function has a vertical stretch by a factor of 3 and is reflected across the y-axis. Is she correct?
f(x)=-2sqrt(x-4)+3
Sally is correct that it's a vertical stretch but it is NOT reflected across the y-axis, it is reflected across the X-AXIS.
In the general formula, what does b do?
g(x)=root(3)(1/b(x-h))+k
b is a horizontal stretch or compression, b < 0 reflection over the y-axis
What are the reference points for this square root function?
f(x)=sqrt(1/4(x+6))+5
(0,0)-->(-6,5)
(1,1)-->(-2,6)
f(x)= root(3)(-1/3(x-4))-9
What are the 3 reference points for this cubic function?
(-1,-1)-->(7,-10)
(0,0)-->(4,-9)
(1,1)-->(1,-8)
What is the domain and range of the following function?
g(x)=-2sqrt(x+4)+5
Decreasing function so
{x|x<=-4}
{y|y<=5}
Sally says the the function has a horizontal compression by a factor of 1/2. Is she correct?
f(x)=root(3)((1/2)x-4)+3
NO!! She is incorrect. b = 2 not 1/2 so there is a horizontal STRETCH by a factor of 2!
If a is negative what happens to the function?
If b is negative what happens to the functions?
If a is negative it is a reflection over the x-axis
if b is negative it is a reflection over the y axis
Write the equation for the square root function (b)reference points shown:
(0,0)-->(1,2)
(1,1)-->(0,3)
f(x)=sqrt(-(x-1))+2
Write the equation for the cube root function using the reference points shown:
f(x) = aroot(3)(x-h)+k
(-1,-1)-->(3,4)
(0,0)-->(4,2)
(1,1)-->(5,0)
f(x)=-2root(3)(x-4)+2
In a square root function what parameters (a,b, h or k) help you find the domain and range?
h helps you find the domain. If the function is decreasing then x is less than or equal to h and if it is increasing x is greater than or equal to h.
k helps you find the range. If the function is decreasing then y is less than or equal to k and if it is increasing y is greater than or equal to k.
What are some common mistakes Sally should make sure to review before she turns in her quiz?
Sally should make sure her h and b values are correct since those are the most common mistakes students make.
Sally should double check her work on the calculator to make sure she doesn't make an arithmetic errors.
Sally should review and be familiar with all her notes so she knows where to find the information before the quiz.