Piecewise Functions
What is the domain and range of the function f(x)=|x|?
Domain: all real numbers
Range: y is greater than or equal to 0
What is 3-3?
Simplify. Write the answer in standard form.
(3x2+4x+2)-(-x+4)
3x2+5x-2
What is the vertex and axis of symmetry for the graph f(x)=x2?
vertex: (0,0)
AOS: x=0
Write an exponential growth or decay function for the following situation: Initial value of 200 increasing at a rate of 5%
What is the difference between a ceiling function and a floor function?
Ceiling function: you round up to the nearest integer
Floor function: you round down to the nearest integer
What is the solution?
16x+2=43x
x=4
Name the polynomial based on its degree and number of terms: 7x3+xy+4
cubic trinomial
How does the value of a affect the graph when compared to the graph of the quadratic parent function?
g(x)=-5x2
more narrow and reflection over x-axis
Write the function of a graph after a shift 1 unit right and 4 units up: f(x)=|x|+2
New function: |x-1|+6
Evaluate: f(x)=ceiling(x); x=11.2
12
The most basic form of an exponential function is f(x)=a*bx. What does a represent?
y-intercept; initial amount; starting amount
Find the product:
(2x-5)(3x2+4x-1)
6x3-7x2-22x+5
What is the vertex and axis of symmetry for the function h(x)=(x+1)2?
Vertex: (-1,0)
AOS: x=-1
What is the common ratio of the geometric sequence?
30, 6, 1.2, 0.24, 0.048...
common ratio is 0.2 or 1/5
Identify the vertex and axis of symmetry:
p(x)=|x|+3
vertex: (0,3)
AOS: x=0
What is the difference between an arithmetic and a geometric sequence?
Arithmetic sequence: numbers are being added or subtracted; has a common difference
Geometric sequence: numbers are being multiplied; has a common ratio
Rewrite in factored form:
x2-11x+10
(x-10)(x-1)
What is the y-intercept of f(x)= -0.3x2-0.6x-0.2?
(0,-0.2)
GCF= 4a4b
How can you reflect the graph of f(x)=3|x+2| across the x-axis?
Make 3 a negative number.
Write an exponential function for the set of points in the form of f(x)=a*bx
(0,3),(1,12),(2,48),(3,192)
f(x)=3*4x
Factor and tell me, what is this special case called?
9x2-100
(3x+10)(3x-10); difference of two squares!
What is the vertex of the function: f(x)=x2+2x+4?
vertex: (-1,3)
Consider the function f(x)=ax2. What happens to the range when a is negative?
Range: y is less than or equal than 0