Arithmetic/Geometric Sequences
Find the next term in the arithmetic sequence:
2,5,8,11,____
14
Describe the transformation: G(x) = x2+5
up 5
What is the inverse of f(x)=x+6
f-1(x)= x-6
Describe the end behavior of this function in limit notation as x goes to infinity: f(x)=x
Positive Infinity
What type of relationship appears as a straight line on a semi-log plot?
Exponential functions
Find the 10th term in the arithmetic sequence:
4,7,10,13
31
Describe the transformation: f(x)= (x-4)2 - 6
right 4, down 6
What is the inverse of f(x)=2x-3
f-1(x)= x+3/2
Describe the end behavior of this function in limit notation as x goes to negative infinity: f(x)= -x3
Positive Infinity
On a semi-log plot, what does the slope of the line represent?
growth or decay rate
Find the 6th term of the geometric sequence:
3,6,12,24....
96
Describe the transformation: g(x)= 3(x−1)2+2
vertical stretch by 3, right 1, up 2
Find the inverse of f(x)=x2 where x≥0
f-1(x)= √x
Describe the end behavior of this function in limit notation: f(x)= 4x7-2x3 +x
Neg. Infinity
A set of data forms a straight line on a semi-log graph. What type of function best models the data?
Exponential Functions
Write an equation for the geometric sequence with the first term:
5,15, 45, 135
an=5(3)n-1
Write a function for f(x) that contains the following:
reflected over the x-axis
shifted right 3 units
shifted down 4 units
g(x)= -(x-3)2 - 4
Are f(x)=3x+1 and g(x)= x-1/3 inverses?
Yes!
Describe end behavior
f(x) = 3x2+1/x2-4
As x goes to positive and negative infinity, the function approaches 3
A function is linear on a semi-log plot and has the equation: log(y)=0.3x+1. Write the function in exponential form.
y=10(1.995)x
Find n if: 3(2n-1 )= 96
6
Describe the transformation:
g(x)= -2(⅓(x+4))2+1
Left 4 units
Horizontal stretch by a factor of 3
Reflect over the x-axis
Vertical stretch by a factor of 2
Up 1 Unit
Find the inverse of f(x)= x-2/x+5
f-1(x)= -2-5x/x-1
Describe end behavior
f(x) = x2+2x+1/x-1
As x goes to pos. and neg. Infinity, the function goes to the slant asymptote y=x+3
A function appears as a line on a semi-log plot and follows log(y)=2x-1. Rewrite the function in the form y=abx
y=1/10(100)x