Question

Write a function G whose graph represents a vertical stretch by a factor of two followed by a translation one unit up of

Answer 1

G(x)=2x+1 , vertical stretch by 2 units and shifted 1 unit up

Given :

Original function f(x)=x

To find :

Function G whose graph is a vertical stretch by 2  and move one unit up

We use the given function to for vertical stretch and shifting up

for Vertical stretch multiply the factor by f(x)

f(x) becomes  2f(x)

so the function becomes 2x

$f(x)=2f(x)=2x$

For moving up , we need to add the units at the end of the function

f(x)+1

2x+1

Hence, G(x)=2x+1

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