Question
upstudy study bank question image url

True or False? Given the function \( f(x)=x^{3} \), the graph of the function \( h(x)=f(x)+10 \) is the graph of \( f(x) \) shifted 10 units vertically upward: Option \#1: True Option \#2: False (1 point) The best answer to the question is Option \# \( \square \).

Ask by Gibbs Chambers. in the United States
Jan 23,2025

Real Tutor Solution

Tutor-Verified Answer

Answer

The best answer is Option #1: True.

Solution

The best answer to the question is Option # 1. **Option #1: True** Adding 10 to \( f(x) \) results in \( h(x) = f(x) + 10 \), which shifts the graph of \( f(x) \) 10 units vertically upward.

Reviewed and approved by the UpStudy tutoring team

error msg
Explain
Simplify this solution

The Deep Dive

True! When you have a function like \( f(x) = x^3 \) and you modify it by adding a constant, such as +10, the overall effect is to lift the entire graph vertically. So, the new function \( h(x) = f(x) + 10 \) results in every point on the original graph moving up by 10 units. It’s like giving your graph a little boost into the sky! Not only is this concept useful in math, but it also appears in real-world situations, like when you’re adjusting the height of a roller coaster or even setting things on different levels in a video game. When you're having fun with functions, remember that adding a constant will shift the graph up or down, while multiplying will stretch or compress it!

Try Premium now!
Try Premium and ask Thoth AI unlimited math questions now!
Maybe later Go Premium
Study can be a real struggle
Why not UpStudy it?
Select your plan below
Premium

You can enjoy

Start now
  • Step-by-step explanations
  • 24/7 expert live tutors
  • Unlimited number of questions
  • No interruptions
  • Full access to Answer and Solution
  • Full Access to PDF Chat, UpStudy Chat, Browsing Chat
Basic

Totally free but limited

  • Limited Solution
Welcome to UpStudy!
Please sign in to continue the Thoth AI Chat journey
Continue with Email
Or continue with
By clicking “Sign in”, you agree to our Terms of Use & Privacy Policy