Vertical Shift of a Linear Function

Question:
The graph of f of x equals 2x is shifted up 5 units to create a new function g of x. Write the equation for g of x and identify the y-intercept of the new function. Then describe how the slope is affected by this transformation.

Vertical Shift of a Linear Function

This lesson explores what happens to a linear function when its graph is shifted vertically. Students learn how adding a constant to a function moves the y-intercept while leaving the slope completely unchanged.

In this lesson, you will learn to:
• Write the equation of a vertically translated linear function by adding a constant to the parent function.
• Identify the new y-intercept after a vertical translation.
• Explain why a vertical translation changes the y-intercept but does not affect the slope.
• Graph both the parent function and the translated function and compare them.

Course: Algebra1 · Big Ideas Math