Instructions
In this worksheet, you will explore vertical translations of functions. For each question, follow the instructions and provide your answers in the spaces provided.
1. Understanding Vertical Translations
A vertical translation occurs when a function is shifted up or down on the coordinate plane. If a function f(x) is translated vertically by k units, the new function can be written as:
g(x) = f(x) + k
or
g(x) = f(x) - k
What does a positive k do to the graph of f(x)? Write your answer below.
What does a negative k do to the graph of f(x)? Write your answer below.
2. Graphing Vertical Translations
Consider the function f(x) = x². Answer the following questions:
a. What is the graph of the function f(x) = x²?
b. Describe the graph of g(x) = x² + 3.
c. Describe the graph of h(x) = x² - 5.
3. Practice Problems
For the following functions, indicate whether the graph is shifted up or down, and by how many units:
a. g(x) = 2x + 4
Shift:
Units:
b. h(x) = -0.5x² - 2
Shift:
Units:
c. k(x) = 3x + 1
Shift:
Units:
4. Application
If you wanted to model the height of a ball thrown into the air, and its height can be represented by the function f(t) = -16t² + 32t, what would the new function be if the entire graph were to rise by 10 units? Write the new function below.
5. Reflection
How do vertical translations affect the maximum or minimum points of a function? Explain your reasoning below.