Question

Is this correct ??????

Answer 1

Answer:
`\bold{b)\quad g(x)=\bigg((1)/(2)\bigg)\bigg5^(x+3)-2}`

Explanation:

`f(x)=a(5)^(b(x-c))+d\\\bullet \text{a is a vertical stretch if }|a|>1\ \text{and a vertical compression if }|a|<1\\\bullet \text{b is a horizontal stretch (or compression)}\\\bullet \text{c is the horizontal shift to right (if positive) and left (if negative)}\\\bullet \text{d is the vertical shift up (if positive) and down (if negative)}`

Vertically compressed by one-half: a =
`(1)/(2)`

Shifted left three units: c = -3

Shifted down two units: d = -2

`g(x)=\bigg((1)/(2)\bigg)\bigg5^(x-(-3))-2`

`\large\boxed{g(x)=\bigg((1)/(2)\bigg)\bigg5^(x+3)-2}`