Write a function g whose graph represents a vertical shrink by a factor of 1/2 of the graph of f(x)=2x+6.

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Write a function g whose graph represents a vertical shrink by a factor of 1/2 of the graph of f(x)=2x+6.

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Math High School Thiên Thanh 3 weeks 2023-01-14T17:32:28+00:00 2023-01-14T17:32:28+00:00 1 Answer 0 views 0

Answer ( 1 )

phucdien · Answer 1 · 2023-01-14T17:33:38+00:00

The function g(x) which is a vertical shrink by a factor of 1/2 of the graph of f(x) is equal to g(x)=x+4.5.

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 graph of f(x)=2x+6 needed to be vertical shrink by a factor of 1/2 is,

g(x) = (1/2) × f(x)

g(x) = (1/2) × (2x + 6)

= [(1/2) ×2x] + [(1/2) ×9]

= x + 4.5

Hence, the function g(x) which is a vertical shrink by a factor of 1/2 of the graph of f(x) is equal to g(x)=x+4.5.

Learn more about Transforming functions here:

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