Problem 60 - College Algebra

Question

What must be done to a function's equation so that its graph is shifted horizontally to the right?

Step-by-Step Solution

Answer

Substitute \(x\) with \((x-d)\) in the given function's equation. Here, \(d > 0\) represents the units by which the graph will shift to the right.

Step 1: Identify the Function

First identify the basic form of the function. For example, if the function is linear, it may appear something like \(f(x) = mx + c\), where \(m\) and \(c\) are constants. The form of the function is crucial because it defines how alterations to the equation will influence the graph.

Step 2: Performing a Horizontal Shift

To execute a horizontal shift to the right of a graph, the transformation can be done by replacing \(x\) with \((x-d)\) in the equation, where \(d > 0\). This will shift the entire graph \(d\) units to the right. The bigger the value of \(d\), the larger the shift.

Step 3: Visualise the Shift

After transforming the equation, the graph can be plotted to visually confirm the shift. For instance, the function \(f(x) = x^2\) would transform into \(f(x) = (x-d)^2\) for a shift to the right, and replotting the new equation will show a definitive shift to the right.