Creative Interpretation Project

Arithmetic/Geometric Sequences

100

Find the next term in the arithmetic sequence:

          2,5,8,11,____  

14

200

Find the 10th term in the arithmetic sequence:

        4,7,10,13 

31

300

Find the 6th term of the geometric sequence: 

        3,6,12,24....

96

400

Write an equation for the geometric sequence with the first term:

         5,15, 45, 135  

 a_n=5(3)^n-1

500

Find n if: 3(2^n-1 )= 96  

6

Function transformations

100

 Describe the transformation: G(x) = x²+5

up 5

200

Describe the transformation: f(x)= (x-4)² - 6  

right 4, down 6

300

Describe the transformation: g(x)= 3(x−1)²+2

vertical stretch by 3, right 1, up 2

400

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

500

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

Inverse Fuctions

100

What is the inverse of f(x)=x+6

f^-1(x)= x-6

200

What is the inverse of f(x)=2x-3

f^-1(x)= x+3/2

                                                                          

300

 Find the inverse of  f(x)=x²   where x≥0  

f^-1(x)= √x

400

Are f(x)=3x+1 and g(x)= x-1/3 inverses?

Yes!

500

 Find the inverse of f(x)= x-2/x+5

 f^-1(x)= -2-5x/x-1

  

End Behavior of Polynomials/Rationals

100

Describe the end behavior of this function in limit notation as x goes to infinity: f(x)=x  

Positive Infinity

200

Describe the end behavior of this function in limit notation as x goes to negative infinity: f(x)= -x³

Positive Infinity

300

 Describe the end behavior of this function in limit notation: f(x)= 4x⁷-2x³ +x

Neg. Infinity

400

Describe end behavior 

f(x) = 3x²+1/x²-4

As x goes to positive and negative infinity, the function approaches 3

500

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

Semi-Log Plots

100

What type of relationship appears as a straight line on a semi-log plot?

Exponential functions

200

On a semi-log plot, what does the slope of the line represent?

growth or decay rate

300

A set of data forms a straight line on a semi-log graph. What type of function best models the data?

Exponential Functions

400

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    

500

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