What is the effect on the graph of the parent function f(x) = x when f(x) is changed to x + 6?

The effect on the graph of the parent function f(x) = x when f(x) is changed to x + 6 will be that the function will move up by 6 units.

How does the transformation of a function happen?

The transformation of a function may involve any change.

Usually, these can be shifted horizontally (by transforming inputs) or vertically (by transforming output), stretched (multiplying outputs or inputs) etc.

If the original function is y = f(x), assuming the horizontal axis is the input axis and the vertical is for outputs, then:

Horizontal shift (also called phase shift):

Left shift by c units, y=f(x+c) (same output, but c units earlier)
Right shift by c units, y=f(x-c)(same output, but c units late)

Vertical shift

Up by d units: y = f(x) + d
Down by d units: y = f(x) - d

Stretching:

Vertical stretch by a factor k: y = k × f(x)
Horizontal stretch by a factor k: y = f(x/k)

Given that the function f(x)=x is transformed to form function g(x)=x+6.

Now, as it is known that any constant value when added to the graph of the function, the graph function moves up by the constant units added, but at the same time if the value of the constant is negative, then the graph moves down by the constant units.

Hence, the effect on the graph of the parent function f(x) = x when f(x) is changed to x + 6 will be that the function will move up by 6 units.

Learn more about Transforming functions here:

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