Now, we can plot these points and connect them with a straight line to have the graph of f(x).
Graph of h(x)
Let's recall the definition of a horizontal translation. When subtracting a number r from a function's input before evaluating, the function translates the graph horizontally.
y=f(x- r)
A value of r less than 0 represents a shift of the original function to the left. Conversely, a value of r greater than 0 means a shift to the right. Because we are given h(x)=f(x+3), we can state that h is a horizontal translation of f. Let's rewrite h(x) to see the direction of the translation.
h(x)=f(x+3)
⇕
h(x)=f(x-( -3))
In this case, r is -3. Since -3<0, h(x) is a horizontal translation 3 units to the left from the graph of f.
