Westonci.ca connects you with experts who provide insightful answers to your questions. Join us today and start learning! Explore thousands of questions and answers from a knowledgeable community of experts ready to help you find solutions. Get quick and reliable solutions to your questions from a community of experienced experts on our platform.
Sagot :
To answer the question, let's start by finding the [tex]\( y \)[/tex]-intercepts of the given functions, [tex]\( g(x) = x + 2 \)[/tex] and [tex]\( f(x) = x - 1 \)[/tex].
### Step-by-Step Solution
1. Find the [tex]\( y \)[/tex]-intercept of [tex]\( g(x) \)[/tex]:
To find the [tex]\( y \)[/tex]-intercept, we need to set [tex]\( x = 0 \)[/tex] in the function [tex]\( g(x) \)[/tex]:
[tex]\[ g(0) = 0 + 2 = 2 \][/tex]
So, the [tex]\( y \)[/tex]-intercept of [tex]\( g(x) \)[/tex] is 2.
2. Find the [tex]\( y \)[/tex]-intercept of [tex]\( f(x) \)[/tex]:
Similarly, we set [tex]\( x = 0 \)[/tex] in the function [tex]\( f(x) \)[/tex]:
[tex]\[ f(0) = 0 - 1 = -1 \][/tex]
So, the [tex]\( y \)[/tex]-intercept of [tex]\( f(x) \)[/tex] is [tex]\(-1\)[/tex].
3. Calculate the difference in [tex]\( y \)[/tex]-intercepts:
To determine how many units below the [tex]\( y \)[/tex]-intercept of [tex]\( g(x) \)[/tex] the [tex]\( y \)[/tex]-intercept of [tex]\( f(x) \)[/tex] is, we subtract the [tex]\( y \)[/tex]-intercept of [tex]\( f(x) \)[/tex] from the [tex]\( y \)[/tex]-intercept of [tex]\( g(x) \)[/tex]:
[tex]\[ \text{Difference in \( y \)-intercepts} = 2 - (-1) = 2 + 1 = 3 \][/tex]
Therefore, the [tex]\( y \)[/tex]-intercept of [tex]\( f(x) \)[/tex] is 3 units below the [tex]\( y \)[/tex]-intercept of [tex]\( g(x) \)[/tex].
Based on this analysis, the correct answer is:
- 3 units
### Step-by-Step Solution
1. Find the [tex]\( y \)[/tex]-intercept of [tex]\( g(x) \)[/tex]:
To find the [tex]\( y \)[/tex]-intercept, we need to set [tex]\( x = 0 \)[/tex] in the function [tex]\( g(x) \)[/tex]:
[tex]\[ g(0) = 0 + 2 = 2 \][/tex]
So, the [tex]\( y \)[/tex]-intercept of [tex]\( g(x) \)[/tex] is 2.
2. Find the [tex]\( y \)[/tex]-intercept of [tex]\( f(x) \)[/tex]:
Similarly, we set [tex]\( x = 0 \)[/tex] in the function [tex]\( f(x) \)[/tex]:
[tex]\[ f(0) = 0 - 1 = -1 \][/tex]
So, the [tex]\( y \)[/tex]-intercept of [tex]\( f(x) \)[/tex] is [tex]\(-1\)[/tex].
3. Calculate the difference in [tex]\( y \)[/tex]-intercepts:
To determine how many units below the [tex]\( y \)[/tex]-intercept of [tex]\( g(x) \)[/tex] the [tex]\( y \)[/tex]-intercept of [tex]\( f(x) \)[/tex] is, we subtract the [tex]\( y \)[/tex]-intercept of [tex]\( f(x) \)[/tex] from the [tex]\( y \)[/tex]-intercept of [tex]\( g(x) \)[/tex]:
[tex]\[ \text{Difference in \( y \)-intercepts} = 2 - (-1) = 2 + 1 = 3 \][/tex]
Therefore, the [tex]\( y \)[/tex]-intercept of [tex]\( f(x) \)[/tex] is 3 units below the [tex]\( y \)[/tex]-intercept of [tex]\( g(x) \)[/tex].
Based on this analysis, the correct answer is:
- 3 units
Thank you for choosing our service. We're dedicated to providing the best answers for all your questions. Visit us again. Thank you for your visit. We're committed to providing you with the best information available. Return anytime for more. Westonci.ca is here to provide the answers you seek. Return often for more expert solutions.