Scaling functions vertically: examples | Transformations of functions | Algebra 2 | Khan Academy

TL;DR

Learn how to graph functions and find the equation of one function in terms of another using tables and key points.

Transcript

• [Instructor] So, we're told that this is the graph of function f right over here. And then they tell us that function g is defined as g of x is equal to one third f of x. What is the graph of g? And if we were doing this on Khan Academy, this is a screenshot from our mobile app, it has multiple choices, but I thought we could just try to sketch i... Read More

Key Insights

• 📈 The graph of g(x) can be obtained by using key points from the graph of f(x) and applying the given transformation.
• 📈 Multiplying f(x) by a constant scales the graph vertically.
• 🚦 Dividing f(x) by a constant compresses the graph in the vertical direction.
• 🍉 The equation of g(x) in terms of f(x) can be found by observing the relationship between their values in a table.
• 😀 Scaling the graph vertically affects all y-values of f(x).
• 📈 Transformations on a graph can be recognized by determining how the function values are altered.
• ⚖️ The absolute value function can be scaled vertically by multiplying its values by a constant.

Questions & Answers

Q: How do you graph the function g(x) when it is equal to one third of f(x)?

To graph g(x), you can use key points from the graph of f(x) and divide the y-values by three. Connect the points to create the graph of g(x).

Q: How do you graph the function g(x) when it is equal to two times the absolute value of f(x) with a negative constant?

To graph g(x), you can use the points from the graph of f(x) and multiply the absolute values by two. Connect the points using straight lines to form the graph of g(x).

Q: How do you find the equation of g(x) in terms of f(x) when g(x) is vertically scaled by a factor of three?

Create a table with x, f(x), and g(x) values. Notice that g(x) is always three times f(x). Therefore, the equation of g(x) in terms of f(x) is g(x) = 3*f(x).

Summary & Key Takeaways

• The video tutorial explains how to graph the function g(x) given that it is equal to one third of the function f(x).

• Another example demonstrates how to graph the function g(x) given that it is equal to two times the absolute value of f(x) with a negative constant.

• A third example shows how to find the equation of g(x) in terms of f(x) when g(x) is vertically scaled by a factor of three.