How do you graph, find the intercepts and state the domain and range of f(x)=1/2(2^x-8)f(x)=12(2x−8)?

1 Answer
Narad T.
Jul 29, 2018

The x-intercept is (3,0)(3,0). The y-intercept is (0,-7/2)(0,−72).
The domain is x in RR. The range is y in (-4,+oo)

Explanation:

The function is

y=1/2(2^x-8)

The intercepts are

when x=0

=>, y=1/2(2^0-8)=1/2(1-8)=-7/2

The y-intercept is (0,-7/2)

when y=0

=>, 0=1/2(2^x-8)

=>, 2^x-8=0

=>, 2^x=2^3

=>, x=3

The x-intercept is (3,0)

The domain is x in RR

To find the range, proceed as follows

y=1/2(2^x-8)

2y=2^x-8

2^x=2y+8

Taking logs

ln(2^x)=ln(2y+8)

xln2=ln(2y+8)

Therefore,

2y+8>0

2y>-8

y>-4

The range is y in (-4,+oo)

See the graph belox

graph{(y-1/2(2^x-8))(y+4)=0 [-14.24, 14.24, -7.12, 7.12]}

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