Please help

Question

describe g(x)=2^x-2-3 as a translation of f(x)=2^x which one would it be?
a) 2 units left and 2 unit down
b)2 units right and 3 units down
c)2 units right 3 unit up
d)2 units left and 3 unit up

Answer 1

g (X) = 2^(X-2) - 3  is an exponential function

 

The general equation for an exponential function is:

 

         Y = ab^(X-h) + k

 

All exponential graphs are translations of the following:

 

                Y = ab^X

 

a is the y-intercept;  b is the base;  X is the exponent, this graph will 

always pass through the point (0,1)  (locator point), and have the 

X-axis as a horizontal asymptote

 

In the general equation:

 

the h value tells you whether to move the basic graph to the right

if h is positive or to the left if h is negative

 

the k value tells you whether to move the graph up if k is positive

or down if k is negative

 

In your problem:

 

 f(X) = 2^X  has been changed to: g(X) = 2^(X-2) - 3

 

  h = 2 graph moves right 2 units; k = -3 graph moves down 3 units

 

Translate the point (0,1) and the whole graph right 2 and down 3

b is your answer

the line Y = -3 will be your horizontal axis