We appreciate your visit to 11 Evaluate the function rule tex f x x 3 2x tex for each value of tex x tex a tex x 3 tex b. This page offers clear insights and highlights the essential aspects of the topic. Our goal is to provide a helpful and engaging learning experience. Explore the content and find the answers you need!
Answer :
Sure, let's work through the problems step-by-step!
11. Evaluate the function rule [tex]\( f(x) = -x^3 + 2x \)[/tex] for each value of [tex]\( x \)[/tex].
a. [tex]\( x=3 \)[/tex]
Calculate:
[tex]\[
f(3) = -(3)^3 + 2 \times 3 = -27 + 6 = -21
\][/tex]
b. [tex]\( x=-2 \)[/tex]
Calculate:
[tex]\[
f(-2) = -(-2)^3 + 2 \times (-2) = 8 - 4 = 4
\][/tex]
---
12. Open-Ended: Describe a situation that models the equation [tex]\( \frac{a}{12}=15 \)[/tex].
This equation can represent a scenario where you have a total number of items, [tex]\( a \)[/tex], evenly divided into groups of 12, and there are 15 such groups. For instance, if you have 15 cartons, each containing 12 eggs, then the total number of eggs is [tex]\( a = 15 \times 12 = 180 \)[/tex].
---
13. The ratio of the length of a side of one square to that of another square is [tex]\( 4:7 \)[/tex]. A side of the smaller square is 12 ft. Find the length of a side of the larger square.
Given ratio [tex]\( 4:7 \)[/tex], if the smaller side is 12 ft, set up the proportion:
[tex]\[
\frac{4}{7} = \frac{12}{\text{larger side}}
\][/tex]
Cross-multiply to solve for the larger side:
[tex]\[
4 \times \text{larger side} = 7 \times 12 \implies \text{larger side} = \frac{84}{4} = 21 \text{ ft}
\][/tex]
---
14. In February, 7 tulips bloom in a garden. In March, 18 tulips bloom. Find the percent change to the nearest percent.
Calculate the percent change using the formula:
[tex]\[
\text{Percent Change} = \left( \frac{\text{New Value} - \text{Old Value}}{\text{Old Value}} \right) \times 100
\][/tex]
[tex]\[
\text{Percent Change} = \left( \frac{18 - 7}{7} \right) \times 100 = \frac{11}{7} \times 100 \approx 157\%
\][/tex]
The percent increase is approximately 157%.
---
15. Draw a scatter plot for T-shirt prices and sales.
16. Draw a speed versus time graph for walking uphill and downhill.
19. Draw graphs of quadratic and absolute value functions on the same axes.
These three require visual representations. You would typically sketch these on graph paper.
---
17. How can you tell whether a graph is a function?
A graph represents a function if every vertical line intersects the graph at most once. This is known as the Vertical Line Test.
---
18. Find the range of the function [tex]\( f(a) = 5 + \frac{1}{2} a \)[/tex] when the domain is [tex]\(\{0, 4, 6\}\)[/tex].
Calculate each value:
- [tex]\( a = 0 \)[/tex]: [tex]\( f(0) = 5 + \frac{1}{2} \times 0 = 5 \)[/tex]
- [tex]\( a = 4 \)[/tex]: [tex]\( f(4) = 5 + \frac{1}{2} \times 4 = 5 + 2 = 7 \)[/tex]
- [tex]\( a = 6 \)[/tex]: [tex]\( f(6) = 5 + \frac{1}{2} \times 6 = 5 + 3 = 8 \)[/tex]
The range is [tex]\(\{5, 7, 8\}\)[/tex].
---
20. What is the probability that a letter of the alphabet picked at random is a vowel (a, e, i, o, or u)?
There are 5 vowels and 26 letters total.
Probability = [tex]\(\frac{\text{Number of Vowels}}{\text{Total Letters}}\)[/tex] = [tex]\(\frac{5}{26}\)[/tex].
---
21. Evaluate [tex]\( y = -x^2 + 7 \)[/tex] for [tex]\( x = -3 \)[/tex].
Calculate:
[tex]\[
y = -(-3)^2 + 7 = -9 + 7 = -2
\][/tex]
---
22. How many times does the graph of [tex]\( y = x^2 - 4 \)[/tex] cross the [tex]\( x \)[/tex]-axis?
Set [tex]\( y = 0 \)[/tex]:
[tex]\[
x^2 - 4 = 0
\][/tex]
[tex]\[
x^2 = 4 \implies x = \pm 2
\][/tex]
The graph crosses the [tex]\( x \)[/tex]-axis at two points, [tex]\( x = 2 \)[/tex] and [tex]\( x = -2 \)[/tex]. So, it crosses twice.
11. Evaluate the function rule [tex]\( f(x) = -x^3 + 2x \)[/tex] for each value of [tex]\( x \)[/tex].
a. [tex]\( x=3 \)[/tex]
Calculate:
[tex]\[
f(3) = -(3)^3 + 2 \times 3 = -27 + 6 = -21
\][/tex]
b. [tex]\( x=-2 \)[/tex]
Calculate:
[tex]\[
f(-2) = -(-2)^3 + 2 \times (-2) = 8 - 4 = 4
\][/tex]
---
12. Open-Ended: Describe a situation that models the equation [tex]\( \frac{a}{12}=15 \)[/tex].
This equation can represent a scenario where you have a total number of items, [tex]\( a \)[/tex], evenly divided into groups of 12, and there are 15 such groups. For instance, if you have 15 cartons, each containing 12 eggs, then the total number of eggs is [tex]\( a = 15 \times 12 = 180 \)[/tex].
---
13. The ratio of the length of a side of one square to that of another square is [tex]\( 4:7 \)[/tex]. A side of the smaller square is 12 ft. Find the length of a side of the larger square.
Given ratio [tex]\( 4:7 \)[/tex], if the smaller side is 12 ft, set up the proportion:
[tex]\[
\frac{4}{7} = \frac{12}{\text{larger side}}
\][/tex]
Cross-multiply to solve for the larger side:
[tex]\[
4 \times \text{larger side} = 7 \times 12 \implies \text{larger side} = \frac{84}{4} = 21 \text{ ft}
\][/tex]
---
14. In February, 7 tulips bloom in a garden. In March, 18 tulips bloom. Find the percent change to the nearest percent.
Calculate the percent change using the formula:
[tex]\[
\text{Percent Change} = \left( \frac{\text{New Value} - \text{Old Value}}{\text{Old Value}} \right) \times 100
\][/tex]
[tex]\[
\text{Percent Change} = \left( \frac{18 - 7}{7} \right) \times 100 = \frac{11}{7} \times 100 \approx 157\%
\][/tex]
The percent increase is approximately 157%.
---
15. Draw a scatter plot for T-shirt prices and sales.
16. Draw a speed versus time graph for walking uphill and downhill.
19. Draw graphs of quadratic and absolute value functions on the same axes.
These three require visual representations. You would typically sketch these on graph paper.
---
17. How can you tell whether a graph is a function?
A graph represents a function if every vertical line intersects the graph at most once. This is known as the Vertical Line Test.
---
18. Find the range of the function [tex]\( f(a) = 5 + \frac{1}{2} a \)[/tex] when the domain is [tex]\(\{0, 4, 6\}\)[/tex].
Calculate each value:
- [tex]\( a = 0 \)[/tex]: [tex]\( f(0) = 5 + \frac{1}{2} \times 0 = 5 \)[/tex]
- [tex]\( a = 4 \)[/tex]: [tex]\( f(4) = 5 + \frac{1}{2} \times 4 = 5 + 2 = 7 \)[/tex]
- [tex]\( a = 6 \)[/tex]: [tex]\( f(6) = 5 + \frac{1}{2} \times 6 = 5 + 3 = 8 \)[/tex]
The range is [tex]\(\{5, 7, 8\}\)[/tex].
---
20. What is the probability that a letter of the alphabet picked at random is a vowel (a, e, i, o, or u)?
There are 5 vowels and 26 letters total.
Probability = [tex]\(\frac{\text{Number of Vowels}}{\text{Total Letters}}\)[/tex] = [tex]\(\frac{5}{26}\)[/tex].
---
21. Evaluate [tex]\( y = -x^2 + 7 \)[/tex] for [tex]\( x = -3 \)[/tex].
Calculate:
[tex]\[
y = -(-3)^2 + 7 = -9 + 7 = -2
\][/tex]
---
22. How many times does the graph of [tex]\( y = x^2 - 4 \)[/tex] cross the [tex]\( x \)[/tex]-axis?
Set [tex]\( y = 0 \)[/tex]:
[tex]\[
x^2 - 4 = 0
\][/tex]
[tex]\[
x^2 = 4 \implies x = \pm 2
\][/tex]
The graph crosses the [tex]\( x \)[/tex]-axis at two points, [tex]\( x = 2 \)[/tex] and [tex]\( x = -2 \)[/tex]. So, it crosses twice.
Thanks for taking the time to read 11 Evaluate the function rule tex f x x 3 2x tex for each value of tex x tex a tex x 3 tex b. We hope the insights shared have been valuable and enhanced your understanding of the topic. Don�t hesitate to browse our website for more informative and engaging content!
- Why do Businesses Exist Why does Starbucks Exist What Service does Starbucks Provide Really what is their product.
- The pattern of numbers below is an arithmetic sequence tex 14 24 34 44 54 ldots tex Which statement describes the recursive function used to..
- Morgan felt the need to streamline Edison Electric What changes did Morgan make.
Rewritten by : Barada
