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Mnenie [13.5K]
2 years ago
14

Please help me out!!!

Mathematics
1 answer:
ehidna [41]2 years ago
5 0

Answer:

Shifts 4 units down ---> g(x)=2x-10

Stretches f(x) by a factor of 4 away from x-axis--->g(x)=8x-6

Shifts f(x) 4 units right---> g(x)=2x-14

Compress f(x) by a factor of 1/4 toward the y-axis ---> g(x)=1/2x-3/2

Step-by-step explanation:

We are given f(x)=2x-6

We need to match the transformations.

1) shifts f(x) 4 units down.

When function f(x) shifts k units down the new function becomes f(x)-k

In our case

g(x)=2x-6-4\\g(x)=2x-10

So, Shifts 4 units down ---> g(x)=2x-10

2) Stretches f(x) by a factor of 4 away from x-axis

When function f(x) is stretched by a factor of b away from x-axis the new function becomes f(bx)

g(x)=2(4x)-6\\g(x)=8x-6

So, Stretches f(x) by a factor of 4 away from x-axis--->g(x)=8x-6

3) Shifts f(x) 4 units right

When function f(x) shifts h units right the new function becomes f(x-h)

g(x)=2(x-4)-6\\g(x)=2x-8-6\\g(x)=2x-14

So,  Shifts f(x) 4 units right---> g(x)=2x-14

4) Compress f(x) by a factor of 1/4 toward the y-axis

When function f(x) is compressed by h factor of a toward the y-axis the new function becomes h.f(x)

g(x)=1/4(2x-6)\\g(x)=1/2x-3/2

Compress f(x) by a factor of 1/4 toward the y-axis ---> g(x)=1/2x-3/2

(Option Not given)

(If we compress f(x) by a factor of 4 towards y-axis we get g(x)=8x-24)

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