Fun with Functions
Sequences and Series
Transform!
100
What is the y-intercept of the following function?
f(x)=sqrt(x^2+9)-8
y=-5
100
What is the common difference of this arithmetic sequence?
5, 9, 13, 17, 21, 25, ...
d=4
100
Describe the transformations applied to the function f.
2f(x-1)
Stretched vertically by 2
Translated right by 1
200
On what intervals is the function below increasing?
(-3,0) and (2,6)
200
What is the recursive definition of this arithmetic sequence?
20, 11, 2, -7, -16, ...
a_n={(20, n=1),(a_(n-1)-9, n>1):}
200
Describe the transformations applied to the function f.
-f(1/3 x)
Reflected over x-axis
Stretched horizontally by 1/3
300
What is the average rate of change of the function below on [-6,6] ?
f(x)={(4x+3, x<=2),(sqrt(x+10), x>2):}
25/12
300
What is the 30th term of this arithmetic sequence?
10, 16, 22, 28, 34, ...
a_(30)=184
300
Describe the transformations applied to the function f.
3/5 f(-x)+8
Compressed vertically by 3/5
Reflected over y-axis
Translated up by 8
400
Write the following absolute value function as a piecewise function.
f(x)=|2x-8|
f(x)={(-2x+8, x<=4),(2x-8, x>4):}
400
Write the following partial sum in sigma notation.
20+15+10+5+0+(-5)
sum_(i=1)^6 (25-5i)
400
Describe the transformations applied to the function f.
1-3/4f(4/3x)
Translated up by 1
Compressed vertically by 3/4
Reflected over x-axis
Compressed horizontally by 4/3
500
CHALLENGE: The following sequence is NOT arithmetic. What is the next term in the sequence?
1, 2, 5, 14, 41, ___
122
Rule: Multiply by 3, then subtract 1
500
CHALLENGE: Describe the transformations applied to the function f.
f(-2x+8)
Reflected over y-axis
Compressed horizontally by 2
Translated right by 4