Domain and Range
What is the domain of a quadratic function?
All real numbers or (-inf, inf)
Given the following functions, find (f+g)(x)
f(x)=2x+1
g(x)=4x-3
6x-2
Draw the following parent functions
1. f(x)=x2
2.g(x)=x3
3.h(x)=|x|
4.m(x)=sqrt(x)
1. "U" shape
2. "S" shape
3. "V" shape
4. Curve starting at origin
Find the solutions of 11|x+3|+9=10
x=-32/11 and x=-34/11
Consider the function f, which is a one-to-one function with values f(8)=-2 and f(-1)=3. What values must be true for the inverse function?
f-1(-2)=8 and f-1(3)=-1
Find the domain and range of the relation
{(11,13), (-24,-17), (18,0), (-1,-16), (-5,-1)}
Domain: {-24,-5, -1, 11, 18}
Range: {-17, -16, -1, 0, 13}
Given the following functions, find g(x)-f(x)
f(x)=-3x+5
g(x)=5x+3
8x-2
Describe the transformation from the parent function to f(x)=(-x)3+2
Reflected across the y-axis and shifted 2 units up
Given the following piecewise function, evaluate f(2)
9
You want to restrict the domain of the function f(x)=|x-2| to make it one-to-one so that it will have an inverse. What are the largest domains, in interval notation, that you could use?
(-inf,2) and (2,inf)
Find the domain of sqrt(2x-40)
[20, inf)
Given the following functions, find (f(x))(g(x))
f(x)=3x2+x-3
g(x)=x+5
3x3+16x2+2x-15
Give me a value of a that would compress the graph of the function f(x)=a(x-2)2+4
Any value between 0 and 1
0<a<1
Given the following piecewise function, evaluate f(0)
3
Use the following table of values for the one-to-one function g(x) to find g-1(-11)
-6
Find the domain of 1/((x-3)(x-2))
All real numbers except 2 and 3
Given the following functions, find g(f(2))
f(x)=4x-4
g(x)=6x+2
26
Describe the transformations that would need to take place to go from f(x)=-1/2(x+1)2-3 back to f(x)=x2
Reflect over the x-axis, stretch by a factor of 1/2, shift 1 unit right and 3 units up.
Graph the piecewise function given
*answer on board*
Give me a point on the graph of the inverse of the function which slope can be found using the following formula:
(7-2)/(3-4)
(2,4) or (7,3)
Use the graph to find its domain and range. Write it in interval notation.
Domain: (-6,5]
Range: [-2,3)
Given the following table of values, find f(g(4))
12
The parent function x4 was reflected over the y-axis, shifted 4 units left and 5 units down. What does that new function look like?
f(x)=(-x+4)4-5
Graph the piecewise function given
*answer on board*
Find the inverse of g(x)=(-x/10)+(7/10)
-10x+7