Question

The exponential function, f(x)=2^x, under goes two transformations to g(x)=1/3•2^x-7. How does the graph change select all that apply

Answer 1

Explanation:

TRANSFORMATIONS:

Vertical shifts:
`f(x)\pm n` Shifts up/down n units

Horizontal shifts:
`f(x\pm n)` Shifts left/right n units

Reflection:
`-f(x)` Reflection over x-axis

Reflection:
`f(-x)` Reflection over y-axis

Dilation:
`f(nx)`

Dilation of x-coordinate n > 1 graph narrows; n < 1 graph widens

Dilation:
`nf(x)`

Dilation of y-coordinate n > 1 graph narrows; n < 1 graph widens.

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We have:

`f(x)=2^x`

`g(x)=(1)/(3)\cdot2^(x-7)=(1)/(3)f(x-7)`

Dilation of y-coordinate (graph widens) and Shifts right 7 units.

look at the picture.