Using Function Notation to Describe Rules (2): IM Alg1.4.5
[url=https://im.kendallhunt.com/HS/teachers/1/4/5/preparation.html]“Using Function Notation to Describe Rules (Part 2)”[/url] from IM Algebra I © 2019 [url=https://www.illustrativemathematics.org/]Illustrative Mathematics[/url]. Licensed under the [url=https://creativecommons.org/licenses/by/4.0/]Creative Commons Attribution 4.0[/url] license.
Table of Contents
- Alg1.4.5 Lesson
- IM Alg1.4.5 Lesson: Using Function Notation to Describe Rules (Part 2)
- Alg1.4.5 Practice
- IM Alg1.4.5 Practice: Using Function Notation to Describe Rules (Part 2)
IM Alg1.4.5 Lesson: Using Function Notation to Describe Rules (Part 2)
[size=100][size=150]Consider the equation [math]q=4+0.8p[/math].[/size][br][br]What value of [math]q[/math] would make the equation true when [math]p[/math] is 7? Explain your reasoning.[/size]
[size=100]What value of [math]q[/math] would make the equation true when [math]p[/math] is 100? [size=100]Explain your reasoning.[/size][/size]
[size=100]What value of [math]p[/math] would make the equation true when [math]q[/math] is 12? [size=100]Explain your reasoning.[/size][/size]
[size=100]What value of [math]p[/math] would make the equation true when [math]q[/math] is 60? [size=100]Explain your reasoning.[/size][/size]
A college student is choosing between two data plans for her new cell phone. Both plans include an allowance of 2 gigabytes of data per month. The monthly cost of each option can be seen as a function and represented with an equation:
[size=150][list][*]Option A: [math]A\left(x\right)=60[/math][/*][*]Option B: [math]B\left(x\right)=10x+25[/math][/*][/list]In each function, the input, [math]x[/math], represents the gigabytes of data used [i]over[/i] the monthly allowance.[/size][br][br][size=100]The student decides to find the values of [math]A\left(1\right)[/math] and [math]B\left(1\right)[/math] and compare them. What are those values?[/size][br]
After looking at some of her past phone bills, she decided to compare [math]A\left(7.5\right)[/math] and [math]B\left(7.5\right)[/math]. What are those values?[br]
Describe each data plan in words.
Graph each function on the same coordinate plane.
Explain which plan you think she should choose.
The student only budgeted $50 a month for her cell phone. She thought, “I wonder how many gigabytes of data I would have for $50 if I go with Option B?” and wrote [math]B\left(x\right)=50[/math]. What is the answer to her question? Explain how you know.[br]
Describe a different data plan that, for any amount of data used, would cost no more than one of the given plans and no less than the other given plan. Explain how you know this data plan would meet these requirements.
The function [math]B[/math] is defined by the equation [math]B\left(x\right)=10x+25[/math]. [br]Use the applet below to find the value of each expression:[br][list][*][math]B(6)[/math][/*][*][math]B(2.75)[/math][/*][*][math]B(1.482)[/math][/*][/list]Use graphing technology to solve each equation:[br][list][*][math]B(x)=93[/math][/*][*][math]B(x)=42.1[/math][/*][*][math]B(x)=116.25[/math][/*][/list]
IM Alg1.4.5 Practice: Using Function Notation to Describe Rules (Part 2)
The cell phone plan from Company C costs $10 per month, plus $15 per gigabyte for data used. The plan from Company D costs $80 per month, with unlimited data.
[size=150]Rule [math]C[/math] gives the monthly cost, in dollars, of using [math]g[/math] gigabytes of data on Company C’s plan. Rule [math]D[/math] gives the monthly cost, in dollars, of using [math]g[/math] gigabytes of data on Company D’s plan.[/size][br][br][size=100]Write a sentence describing the meaning of the statement [math]C\left(2\right)=40[/math].[/size]
Which is less, [math]C\left(4\right)[/math] or [math]D\left(4\right)[/math]? What does this mean for the two phone plans?[br]
Which is less, [math]C\left(5\right)[/math] or [math]D\left(5\right)[/math]? Explain how you know.[br]
For what number [math]g[/math] is [math]C\left(g\right)=130[/math]?[br]
Draw the graph of each function.
[size=150]Function [math]g[/math] is represented by the graph.[br][br][img]data:image/png;base64,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[/img][br][size=100]For what input value or values is [math]g\left(x\right)=4[/math]?[/size][/size]
[size=150]Function [math]P[/math] gives the perimeter of an equilateral triangle of side length [math]s[/math]. It is represented by the equation [math]P\left(s\right)=3s[/math]. [/size][br][br][size=100]What does [math]P\left(s\right)=60[/math] mean in this situation?[/size]
Find a value of [math]s[/math] to make the equation [math]P(s)=60[/math] true.
[size=100][size=150]Function [math]G[/math] takes a student’s first name for its input and gives the number of letters in the first name for its output. [br][/size][br]Describe the meaning of [math]G\left(Jada\right)=4[/math].[br][/size]
Find the value of [math]G\left(Diego\right)[/math].
[size=100][size=150][math]W[/math] gives the weight of a puppy, in pounds, as a function of its age, [math]t[/math], in months. Describe the meaning of each statement in function notation:[/size][br][br][math]W\left(2\right)=5[/math][/size]
[math]W\left(6\right)[/math]>[math]W\left(4\right)[/math]
[math]W\left(12\right)=W\left(15\right)[/math]
Diego is building a fence for a rectangular garden. It needs to be at least 10 feet wide and at least 8 feet long. The fencing he uses costs $3 per foot. His budget is $120.
[size=150]He wrote some inequalities to represent the constraints in this situation.[br]Explain what each equation or inequality represents:[/size][br][br][math]f=2x+2y[/math][br]
[math]x\ge10[/math]
[math]y\ge8[/math]
[math]3f\le120[/math]
His mom says he should also include the inequality [math]f>0[/math]. Do you agree? Explain your reasoning.[br]