GOZUNTA
Try it now
All courses Math I · F-BF.3 18 of 59
Analyze graph transformations caused by f(x)+k, kf(x), f(kx), and f(x+k); identify even/odd functions.

Describe a vertical shift of a function

Problem
Describe the vertical shift from f(x) to f(x)+4.
Your answer
With a free account

Choose exactly what to practice.

Browse the learning objectives and included problem types, then build a session around the math you want to work on.

Create a free account
With paid access

Use the complete visual-support library.

Paid access opens the visual supports attached throughout the full problem bank in your subscribed course or courses.

Compare plans

Hint

Notice that the +4 is added after f(x), so it changes the output values rather than the input values.

Adding a number outside f(x) changes the output values. A positive outside number raises every y-value by that amount.

Solution walkthrough

01

Locate the change

\[f(x)~->~f(x)~+~4\]

The +4 is outside the function value, so it is added to the output after f(x) is evaluated.

02

Interpret the output change

\[\text{new}~\text{output}~=~\text{old}~\text{output}~+~4\]

Adding 4 to the output makes every y-value 4 greater than it was on the graph of f.

03

Describe the shift

\[\text{shift}~\text{up}~4~\text{units}\]

Increasing every y-value by the same positive amount moves the graph straight upward.

04

State the answer

\[f(x)~\text{to}~f(x)~+~4:~\text{shift}~\text{up}~4~\text{units};~\text{every}~\text{output}~\text{increases}~\text{by}~4\]

This states both the graph movement and what happens to the outputs.

+

Another way

  1. Check any point on the original graph. If (x, y) is on y = f(x), then (x, y + 4) is on y = f(x) + 4, so the whole graph moves up 4 units.

!

Common mistake

A common mistake is to call f(x) + 4 a horizontal shift. Because the 4 is added outside the function, it changes y-values and makes a vertical shift.