Answer:
Part A;
k = -1
Part B
k = -4
Part C
g(x) = 3ˣ - 1
h(x) = [tex]3^{x - 4}[/tex]
Explanation:
The parent function of the graph, is f(x) = 3ˣ
Part A;
g(x) = f(x) + k
When x = 0, f(x) = 3⁰ = 1
g(x) = f(x) + k = [tex]3 ^{x}[/tex] + k
Therefore;
When x = 0, g(0) = f(0) + k = [tex]3 ^{0}[/tex] + k = k
From the graph, g(0) = -1, therefore;
g(0) = -1 = k
k = -1
Part B
h(x) = f(x + k)
When x = 4, h(4) = f(4 + k) = [tex]3 ^{(4 + k)}[/tex]
From the graph, h(4) = 1, therefore;
h(4) = 1 = [tex]3 ^{(4 + k)}[/tex]
Therefore, we get;
ln(1) = (4 + k)·ln(3)
4 + k = ln(1)/ln(3) = 0
k = 0 - 4 = -4
k = -4
Part C
g(x) = f(x) + k
f(x) = 3ˣ, and k = -1
Therefore;
g(x) = 3ˣ - 1
h(x) = f(x + k)
f(x) = 3ˣ, and k = -4
Therefore;
h(x) = [tex]3^{x - 4}[/tex]
