Unit 2: Transformations, Compositions, and Inverses of Functions

Function Transformations

100

When the a-value is greater than 1

What is vertical stretch?

200

lx-5l+3 Which number moves the graph up?

What is 3?

300

Write the function from the parent y=lxl with a grap that is right 2, up 4 and has a vertical stretch of 2.

What is 2lx-2l+4?

400

4lx+2l-5 What transformations have been done to this equation?

What is vertical stretch by 4, left 2, and down 5?

500

How does a graph become reflected across the x axis?

What is changing the a value to a negative number?

Combining Functions

100

g(x) = 2x+5

h(x) = x²

^{Find g(h(3))}

What is 23?

200

g(x) = 2x+5

h(x) = x²

^{Find h(g(3))}

What is 121?

300

Find  g(f(x)) when: f(x)=x²+1 and g(x)=2x

What is 2(x²+1)

400

For the expression 2(x-3)²+5 and given that this is f(g(x)), 

Find f(x).  

What is 2x +5

500

f(x)=4x-3 g(x)=x²+1 What is g(f(2))?

What is 26?

Inverses

100

The inverse of a function switches the ___ and ___ values.

What is x and y?

200

Find the inverse of the function -4x+12.

What is (x-12)/4?

300

Find the inverse of the function: y=3x+3.

What is y = (x-3)/3?

400

If the inverse of the function is also a function, it is defined as __________.

What is one-to-one.

500

Let f(x) = 2x-1 and g(x) = 2x+1

Find whether or not they are inverses.

What is no?

Using a Table

100

x   f(x)    g(x)

2    -5     4

1    -2     2

4     3     1

Using the table above, h(x) = 3f(x) + 5, find h(2)

What is 0?

200

x   f(x)    g(x)

2    -5     4

1    -2     2

4     3     1

Using the table above, f(4)+g(1)

What is 5?

300

x   f(x)    g(x)

2    -5     4

1    -2     2

4     3     1

Using the table above, f(g(1))

What is -5?

400

x   f(x)    g(x)

2    -5     4

1    -2     2

4     3     1

What is f inverse of 3?

What is 4?

500

x   f(x)    g(x)

2    -5     4

1    -2     2

4     3     1

Find g(g(4)).

What is 2?

Miscellaneous

100

Find the parent function that looks like a letter from the alphabet. 

What is absolute value?

200

Solve the equation for x.  

|x-3|+5=8

What are 0 and 6?

300

The graph of the inverse is always a reflection of the original graph over the line ______.

What is y=x?

400

The slopes of these two lines are 3/5 and -5/3.   Find the relationship between the two lines. 

What is perpendicular?

500

When is an equation not considered a function?

What is failing the vertical line test/ having two y-values for one x-value?