Asksia AI LOGO

Sia

Question
Math
Posted 2 months ago

Starting with the graph of f(x)=9xf(x)=9^{x}, write the equation of the graph that results when:
(a) f(x)f(x) is shifted 5 units downward. y=y=
(b) f(x)f(x) is shifted 2 units to the left. y=y=
(c) f(x)f(x) is reflected about the xx - axis. y=y=
Sign in to unlock the answer
Answer from Sia
Posted 2 months ago
Solution by Steps
step 1
Start with the original function: f(x)=9xf(x) = 9^x
step 2
To shift the function 5 units downward, subtract 5 from the function: y=9x5y = 9^x - 5
Answer
y=9x5y = 9^x - 5


 (b) f(x)f(x) is shifted 2 units to the left. y=y=
step 1
Start with the original function: f(x)=9xf(x) = 9^x
step 2
To shift the function 2 units to the left, replace xx with x+2x + 2: y=9x+2y = 9^{x + 2}
Answer
y=9x+2y = 9^{x + 2}


 (c) f(x)f(x) is reflected about the xx-axis. y=y=
step 1
Start with the original function: f(x)=9xf(x) = 9^x
step 2
To reflect the function about the xx-axis, multiply the function by 1-1: y=9xy = -9^x
Answer
y=9xy = -9^x
Key Concept
Graph Transformations
Explanation
Shifting a graph vertically involves adding or subtracting a constant to the function. Shifting horizontally involves replacing xx with x+cx + c or xcx - c. Reflecting about the xx-axis involves multiplying the function by 1-1.

Not the question you are looking for? Ask here!

Enter question by text

Enter question by image

Upgrade to Asksia Pro

Join a AskSia's Pro Plan, and get 24/7 AI tutoring for your reviews, assignments, quizzes and exam preps.

Unlimited chat query usages
Strong algorithms that better know you
Early access to new release features
Study Other Question