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How do you describe the transformation in #y=2^(x-3)#?

Answer 1

The form is # y=a b^x#, with #a = 1/8 and b = 2. The plot of {(x, Y)}, with Y = log y, on a semi-log graph paper will be a straight line,.

This is an exponential transformation, of the form #y=a b^x#.

A short Table for making the graph for

#y=2^(x-3)=(1/8)(2^x)#

is given below.

#(x, y): ... (-4,1/128) (-3, 1/64) (-2, 1/32) (-1, 1/16)#

#(0, 1/8) (1, 1/4) (2, 1/2) (3, 1) (4, 2)....(N, 2^(N-3)) ...#

Equating logarithms, #Y=log y =x log 2 - 3 log 2#

The plot of [{x, Y)}, with Y= log y, on a semi-log graph paper, will be a

straight line.

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Answer 2

Madelyn Anderson

The transformation in the function ( y = 2^{x-3} ) involves a horizontal shift of 3 units to the right compared to the parent function ( y = 2^x ).

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.