Question
Starting with the graph of \( f(x)=8^{x} \), write the formula for the function that results from (a) shifting \( f(x) 4 \) units downward. \( y=\square \) (b) shifting \( f(x) 7 \) units to the right. \( y=\square \) (c) reflecting \( f(x) \) about the x-axis and the y-axis. \( y=\square \)
Ask by Lane Reed. in the United States
Mar 01,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
(a) \( y = 8^{x} - 4 \)
(b) \( y = 8^{x - 7} \)
(c) \( y = -8^{-x} \)
Solution
We start with the function f(x) = 8ˣ.
(a) To shift the graph 4 units downward, subtract 4 from f(x):
y = 8ˣ - 4
(b) To shift the graph 7 units to the right, replace x with (x - 7):
y = 8^(x - 7)
(c) Reflecting the graph about the x-axis multiplies f(x) by -1, and reflecting it about the y-axis replaces x with -x. Applying both transformations gives:
y = -8^(-x)
Answered by UpStudy AI and reviewed by a Professional Tutor
Like
error msg
Explain 
Simplify this solution Extra Insights
To shift the graph of \( f(x) = 8^x \) downward by 4 units, you would subtract 4 from the function. Thus, the new function is: \( y = 8^x - 4 \) For shifting the graph 7 units to the right, you would replace \( x \) with \( x - 7 \). Therefore, the function becomes: \( y = 8^{(x - 7)} \) Reflecting the graph about the x-axis inverts the function and reflecting it about the y-axis changes the sign of \( x \). Thus, the combined reflection yields: \( y = -8^{-x} \)
