Question

homework assignment 6.2 graphs of exponential functio
due sunday by 11:59pm points 10 submitting an external tool
homework assignment 6.2 graphs of exponential functions
score: 3.4/10 answered: 4/10
question 5
starting with the graph of ( f(x)=4^{x} ), write the equation of the graph that results when:
(a) ( f(x) ) is shifted 6 units upward. ( y=)
(b) ( f(x) ) is shifted 8 units to the right. ( y=)
(c) ( f(x) ) is reflected about the ( x )-axis and the ( y )-axis. ( y=)
question help: video read written example

Explanation:

Step1: Vertical shift formula

For a function \(y = f(x)\), shifting \(k\) units upward gives \(y=f(x)+k\). Here \(f(x) = 4^{x}\) and \(k = 6\), so \(y=4^{x}+6\).

Step2: Horizontal shift formula

For a function \(y = f(x)\), shifting \(h\) units to the right gives \(y = f(x - h)\). Here \(f(x)=4^{x}\) and \(h = 8\), so \(y = 4^{x - 8}\).

Step3: Reflection about axes formula

Reflection about the \(x\) - axis: \(y=-f(x)\); reflection about the \(y\) - axis: \(y = f(-x)\). First reflect about \(x\) - axis: \(y=-4^{x}\), then reflect about \(y\) - axis: \(y=-4^{-x}\).

Answer:

(a) \(y = 4^{x}+6\)
(b) \(y = 4^{x - 8}\)
(c) \(y=-4^{-x}\)