an exponential function f(x) = b^x can be transformed to the general exponential

Question

an exponential function f(x) = b^x can be transformed to the general exponential function g(x) = ab^(x – h) + k. Complete the following to describe how the parameters a, h, and k transform the graph of f(x) to give the graph of g(x).

a.If h > 0, the graph of f(x):

b.If h < 0, the graph of f(x):

c.If a > 1, the graph of f(x):

d.If 0 < a < 1, the graph of f(x):

e.If –1 < a < 0, the graph of f(x):

f.If a < –1, the graph of f(x):

g.If k > 0, the graph of f(x):

h.If k < 0, the graph of f(x):

i.If a > 0, the range of g(x):

j.If a < 0, the range of g(x):

Explanation / Answer

f(x) = ab^x

g(x) = ab^(x-h) + k

a) if h > 0 , the graph of f(x) is transformed horizontally to h units right

b) if h<0 , the graph of f(x) is transoformed horizontally to h units left

c) if a>1 , the graph is exponentially increasing

d) if 0<a<1 , the graph is constant

e) if -1<a<0 , the graph is constant but on negative y axis

f) a<-1, the graph is exponentially decreasing

g) if k >0 , the graph is shifted vertically upwards k units

h) if k < 0 , the graph is shifted vertically downwards k units

i) if a>0 , the range of g(x) is all values of y greater than k

j) if a<0 , the range of g(x) is all velues of y less than k

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