Question

name
date
pd
precalculus chapter 1.5 transformation of functions
directions: read all questions carefully. use the online textbook to check any odd numbered
questions from chapter 1.5:
https://openstax.org/books/precalculus-2e/pages/1-5-transformation-of-functions

1. write a formula for the function obtained when the graph of ( f(x)=sqrt{x} ) is shifted up 1 unit and to the left 2

units.

1. write a formula for the function obtained when the graph of ( f(x)=|x| ) is shifted down 3 units and to the

right 1 unit.

1. write a formula for the function obtained when the graph of ( f(x)=\frac{1}{x} ) is shifted down 4 units and to the

right 3 units.

1. write a formula for the function obtained when the graph of ( f(x)=\frac{1}{x^{2}} ) is shifted up 2 units and to the left 4

units.
for the following exercises, describe how the graph of the function is a transformation of the graph of the original
function ( f ).

1. ( y=f(x - 49) )
2. ( y=f(x + 43) )
3. ( y=f(x + 3) )
4. ( y=f(x - 4) )
5. ( y=f(x)+5 )
6. ( y=f(x)+8 )
7. ( y=f(x)-2 )
8. ( y=f(x)-7 )
9. ( y=f(x - 2)+3 )
10. ( y=f(x + 4)-1 )

Explanation:

Problem 6

Step1: Shift left 2 units

Replace $x$ with $x+2$: $\sqrt{x+2}$

Step2: Shift up 1 unit

Add 1 to the function: $\sqrt{x+2} + 1$

Step1: Shift right 1 unit

Replace $x$ with $x-1$: $|x-1|$

Step2: Shift down 3 units

Subtract 3 from the function: $|x-1| - 3$

Step1: Shift right 3 units

Replace $x$ with $x-3$: $\frac{1}{x-3}$

Step2: Shift down 4 units

Subtract 4 from the function: $\frac{1}{x-3} - 4$

Answer:

$\sqrt{x+2} + 1$

Problem 7