We are asked to find a transformation that moves the graph of f(x)=x^5-3x^4+2x-4 to a graph with a y-intercept of - 2.
We can do this by moving any point on the graph of f to the point (0,2).
Let's calculate f(0) to find the y-intercept of the graph of f.
A translation up by 2 units moves the point (0,-4) to (0,-2), so it moves the graph of f to a graph with a y-intercept at -2.
Let's find the equation of the new graph.
To represent a translation up by 2 units we need to add 2 to f(x).
The diagram below illustrates the two graphs and the transformation.
Alternative Solution
Alternative way of thinking
As mentioned in the solution, any point on the graph of f can be translated to the y-axis to become the y-intercept of the transformed graph.
For example, if we translate the graph 2 units to the left and 14 units up, then the point (2,-16) of the graph of f becomes the y-intercept at - 2 of the transformed graph.
