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

Question

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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3 weeks 2023-01-14T17:32:28+00:00 1 Answer 0 views 0

Answer ( 1 )

1. 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.