Question

Consider the following. the parent function is f(x)=3^x.

Answer 1

Answer:

Part A;

k = -1

Part B

k = -4

Part C

g(x) = 3ˣ - 1

h(x) = $3^{x - 4}$

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 = $3 ^{x}$ + k

Therefore;

When x = 0, g(0) = f(0) + k = $3 ^{0}$  + 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) = $3 ^{(4 + k)}$  

From the graph, h(4) = 1, therefore;

h(4) = 1 = $3 ^{(4 + k)}$

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) = $3^{x - 4}$