Question

Each statement describes a transformation of the graph of y = log2x. Which statement correctly describes the graph of y = log2(x + 3) - 9?

Answer 1

The transformation of a function may involve any change in the initial function. The correct option is C.

The complete question is:

Each statement describes a transformation of the graph of y = log2x.

Which statement correctly describes the graph of y = log2(x + 3) - 9?

• It is the graph of y = log2x translated 3 units down and 9 units to the left.
• It is the graph of y = log2x translated 9 units down and 3 units to the right.
• It is the graph of y = log2x translated 9 units down and 3 units to the left.
• It is the graph of y = log2x translated 3 units up and 9 units to the left.

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: $y = k \times f(x)$
• Horizontal stretch by a factor k: $y = f(\dfrac{x}{k})$

Given the initial function y = log2x, now if the function is needed to be transformed to y = log2(x + 3) - 9, then the function is needed to be shifted left by 3 units and down by 9 units.

Hence, the correct option is C.

Learn more about Transforming functions:

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