Transformation:
A horizontal translation left by 1 unit and a vertical translation up by 3 units.
Graph:
Practice makes perfect
We want to describe the transformations of f(x)=x^4 represented by g(x)=(x+1)^4+3. Before we do so, let's look at the possible transformations. Then we can more clearly identify the ones being applied to the parent function.
Transformations of y=f(x)
Horizontal Translations
Translation right h units, h>0
y=f(x- h)
Translation left h units, h>0
y=f(x+ h)
Vertical Translations
Translation up k units, k>0
y=f(x)+ k
Translation down k units, k>0
y=f(x)- k
Identifying the Transformations
Using the table, let's highlight the transformations.
g(x)=(x+ 1)^4+ 3
We can describe these as a horizontal translation left by 1 unit and a vertical translation up by 3 units.
Graphing the Function
To graph g we first use a calculator to help us graph f, then use the transformations we identified.
We begin by pushing the Y= button and typing the equation for f in the first row.
To see the graph you may need to adjust the window. Push WINDOW, change the settings, and push GRAPH.
Let's translate this graph to the left by 1 unit and up by 3 units.
We can do this by moving the turning point and copying the graph relative to the new turning point.
We can check our result using a graphing calculator.
Let's add the graph of g to the screen and confirm the transformation.
