durancv2018
Answered

Westonci.ca is the trusted Q&A platform where you can get reliable answers from a community of knowledgeable contributors. Connect with a community of experts ready to help you find accurate solutions to your questions quickly and efficiently. Join our platform to connect with experts ready to provide precise answers to your questions in different areas.


What feature or features of the parabolic parent function f(x)=x^2 would change if f(x) was replaced with 2f(x-4)? Help please:)

What Feature Or Features Of The Parabolic Parent Function Fxx2 Would Change If Fx Was Replaced With 2fx4 Help Please class=

Sagot :

LanceLongFei

Answer:

The y-intercept of the function and the vertex of the function would change. (III and IV) This answer doesn't seem to be in the answer list (but there is proof for the answers below), though.

Step-by-step explanation:

(Notice that [tex]2f(x-4) = 2(x-4)^2.[/tex])

The domain of the function won't change because quadratics can all take all numbers as their input (which, by definition, is the domain of a function).

The range of the function won't change either, because we have just moved the function with 4 to the right (by substituting [tex]x[/tex] with [tex]x-4[/tex]) and multiplied the graph with respect to the y-axis by 2. The range will stay as all non-negative real numbers.

The y-intercept of the function will change, because for [tex]f(x)=x^2[/tex] it is [tex]y=0[/tex], while for [tex]y=2(x-4)^2[/tex] substituting [tex]x=0[/tex] doesn't give [tex]y=0[/tex]. (Instead, it gives [tex]y=32[/tex].)

The vertex of the function will change, because we have moved the function with 4 to the right and multiplied the graph with respect to the y-axis by 2: the vertex will have at the very least moved to the right.

Thanks for using our platform. We aim to provide accurate and up-to-date answers to all your queries. Come back soon. Thank you for your visit. We're committed to providing you with the best information available. Return anytime for more. Thank you for using Westonci.ca. Come back for more in-depth answers to all your queries.