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

Step-by-step 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:

$f(x)=2^x$

$g(x)=\dfrac{1}{3}\cdot2^{x-7}=\dfrac{1}{3}f(x-7)$

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

look at the picture.