Answered

Welcome to Westonci.ca, your one-stop destination for finding answers to all your questions. Join our expert community now! Explore a wealth of knowledge from professionals across various disciplines on our comprehensive Q&A platform. Experience the ease of finding precise answers to your questions from a knowledgeable community of experts.

Unit Activity: Functions

1. Solve the following:

[tex]\[
\begin{tabular}{|c|c|}
\hline
-2 & 76 \\
\hline
-1 & 11 \\
\hline
0 & -4 \\
\hline
1 & 5 \\
\hline
2 & -4 \\
\hline
3 & 11 \\
\hline
\end{tabular}
\][/tex]

2. Given the function [tex]\(k(x) = x^4 + 2x^2 + 8x - 4\)[/tex]:

Select the correct answer from each drop-down:

- The function that has the least minimum value is function [tex]\(\square\)[/tex]
- The function that has the greatest minimum value is function [tex]\(\square\)[/tex]

Sagot :

GinnyAnswer
Let's solve the problem step-by-step:

1. Define the functions:
- The function [tex]\( h(x) \)[/tex] is given by:
[tex]\[ h(x) = 2(x - 7)^2 \][/tex]
- The function [tex]\( k(x) \)[/tex] is given by:
[tex]\[ k(x) = x^4 + 2x^2 + 8x - 4 \][/tex]

2. Evaluate [tex]\( h(x) \)[/tex] and [tex]\( k(x) \)[/tex] for given [tex]\( x \)[/tex] values:
- The provided [tex]\( x \)[/tex] values are: [tex]\( -2, -1, 0, 1, 2, 3 \)[/tex]

3. Evaluate [tex]\( h(x) \)[/tex] for each [tex]\( x \)[/tex]:
- [tex]\( h(-2) = 2(-2 - 7)^2 = 2(-9)^2 = 2 \times 81 = 162 \)[/tex]
- [tex]\( h(-1) = 2(-1 - 7)^2 = 2(-8)^2 = 2 \times 64 = 128 \)[/tex]
- [tex]\( h(0) = 2(0 - 7)^2 = 2(-7)^2 = 2 \times 49 = 98 \)[/tex]
- [tex]\( h(1) = 2(1 - 7)^2 = 2(-6)^2 = 2 \times 36 = 72 \)[/tex]
- [tex]\( h(2) = 2(2 - 7)^2 = 2(-5)^2 = 2 \times 25 = 50 \)[/tex]
- [tex]\( h(3) = 2(3 - 7)^2 = 2(-4)^2 = 2 \times 16 = 32 \)[/tex]

4. Evaluate [tex]\( k(x) \)[/tex] for each [tex]\( x \)[/tex]:
- [tex]\( k(-2) = (-2)^4 + 2(-2)^2 + 8(-2) - 4 = 16 + 8 - 16 - 4 = 4 \)[/tex]
- [tex]\( k(-1) = (-1)^4 + 2(-1)^2 + 8(-1) - 4 = 1 + 2 - 8 - 4 = -9 \)[/tex]
- [tex]\( k(0) = 0^4 + 2(0)^2 + 8(0) - 4 = -4 \)[/tex]
- [tex]\( k(1) = 1^4 + 2(1)^2 + 8(1) - 4 = 1 + 2 + 8 - 4 = 7 \)[/tex]
- [tex]\( k(2) = 2^4 + 2(2)^2 + 8(2) - 4 = 16 + 8 + 16 - 4 = 36 \)[/tex]
- [tex]\( k(3) = 3^4 + 2(3)^2 + 8(3) - 4 = 81 + 18 + 24 - 4 = 119 \)[/tex]

5. Identify the minimum values of each function:
- The minimum value of [tex]\( h(x) \)[/tex] from the computed values is [tex]\( 32 \)[/tex].
- The minimum value of [tex]\( k(x) \)[/tex] from the computed values is [tex]\( -9 \)[/tex].

6. Determine which function has the least and greatest minimum value:
- The function with the least minimum value is [tex]\( k(x) \)[/tex] because [tex]\( -9 \)[/tex] is less than [tex]\( 32 \)[/tex].
- The function with the greatest minimum value is [tex]\( h(x) \)[/tex] because [tex]\( 32 \)[/tex] is greater than [tex]\( -9 \)[/tex].

Based on these steps, we can complete the statements:

- The function that has the least minimum value is function [tex]\( k(x) \)[/tex].
- The function that has the greatest minimum value is function [tex]\( h(x) \)[/tex].
Thank you for visiting our platform. We hope you found the answers you were looking for. Come back anytime you need more information. We appreciate your time. Please come back anytime for the latest information and answers to your questions. Thank you for visiting Westonci.ca, your go-to source for reliable answers. Come back soon for more expert insights.