lizziefufu2
Answered

Discover the best answers at Westonci.ca, where experts share their insights and knowledge with you. Discover a wealth of knowledge from professionals across various disciplines on our user-friendly Q&A platform. Get precise and detailed answers to your questions from a knowledgeable community of experts on our Q&A platform.

If [tex]$y = 12x - 7$[/tex] were changed to [tex]$y = 12x + 1$[/tex], how would the graph of the new function compare with the original?

A. It would be less steep.
B. It would be shifted down.
C. It would be steeper.
D. It would be shifted up.

Sagot :

GinnyAnswer
To compare the graphs of the original function [tex]\( y = 12x - 7 \)[/tex] with the new function [tex]\( y = 12x + 1 \)[/tex], we need to examine their slopes and y-intercepts:

1. Examine the slopes:
- The slope of the original function [tex]\( y = 12x - 7 \)[/tex] is [tex]\( 12 \)[/tex].
- The slope of the new function [tex]\( y = 12x + 1 \)[/tex] is also [tex]\( 12 \)[/tex].

Since both functions have the same slope, they are equally steep. Therefore, options A and C are incorrect because the steepness does not change.

2. Examine the y-intercepts:
- The y-intercept of the original function is [tex]\( -7 \)[/tex].
- The y-intercept of the new function is [tex]\( +1 \)[/tex].

The change in the y-intercept from [tex]\( -7 \)[/tex] to [tex]\( +1 \)[/tex] indicates a vertical shift. Since the new y-intercept [tex]\( +1 \)[/tex] is greater than the original y-intercept [tex]\( -7 \)[/tex], the graph of the new function shifts upward.

Therefore, the correct answer is:
D. It would be shifted up.
We appreciate your time on our site. Don't hesitate to return whenever you have more questions or need further clarification. Your visit means a lot to us. Don't hesitate to return for more reliable answers to any questions you may have. Westonci.ca is committed to providing accurate answers. Come back soon for more trustworthy information.