IM Alg1.4.4 Lesson: Using Function Notation to Describe Rules (Part 1)
What do you notice? What do you wonder?
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[/img] 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[/img]
Here are descriptions and equations that represent four functions.
Match each equation with a verbal description that represents the same function. Record your results.[br][math]f\left(x\right)=3x-7[/math]
[math]g\left(x\right)=3\left(x-7\right)[/math]
[math]h\left(x\right)=\frac{x}{3}-7[/math]
[math]k\left(x\right)=\frac{x-7}{3}[/math]
For one of the functions above, when the input is 6, the output is -3. Which is that function: [math]f[/math], [math]g[/math], [math]h[/math], or [math]k[/math]? Explain how you know.[br]
Which function value— [math]f\left(x\right),g\left(x\right),h\left(x\right)[/math], or [math]k\left(x\right)[/math]—is the greatest when the input is 0?
Which function value— [math]f\left(x\right),g\left(x\right),h\left(x\right)[/math], or [math]k\left(x\right)[/math]—is the greatest when the input is 10?
Mai says [math]f\left(x\right)[/math] is always greater than [math]g\left(x\right)[/math] for the same value of [math]x[/math]. Is this true? Explain how you know.
A square that has a side length of 9 cm has an area of 81 cm² . The relationship between the side length and the area of the square is a function. Complete the table with the area for each given side length.
Then, write a rule for a function, [math]A[/math], that gives the area of the square in cm² when the side length is [math]s[/math] cm. Use function notation.
What does [math]A(2)[/math] represent in this situation? What is its value?
On the coordinate plane, sketch a graph of this function.
A roll of paper that is 3 feet wide can be cut to any length.
[br][table][tr][td]If we cut a length of 2.5 feet, what is the perimeter of the paper?[/td][td][img]data:image/png;base64,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[/img][/td][/tr][/table]
Complete the table with the perimeter for each given side length.
Then, write a rule for a function, [math]P[/math], that gives the perimeter of the paper in feet when the side length in feet is [math]\ell[/math]. Use function notation.
What does [math]P(11)[/math] represent in this situation? What is its value?[br]
On the coordinate plane, sketch a graph of this function.
IM Alg1.4.4 Practice: Using Function Notation to Describe Rules (Part 1)
Match each equation with a description of the function it represents.
[math]f\left(x\right)=2x+4[/math]
[math]g\left(x\right)=2\left(x+4\right)[/math]
[math]h\left(x\right)=4x+2[/math]
[math]k\left(x\right)=4\left(x+2\right)[/math]
Function P represents the perimeter, in inches, of a square with side length x inches. Complete the table.
Write an equation to represent function [math]P[/math].[br]
Sketch a graph of function P.
Functions f and A are defined by these equations.
[table][tr][td][math]f\left(x\right)=80-15x[/math] [/td][td] [math]A\left(x\right)=25+10x[/math][br][/td][/tr][/table] Which function has a greater value when [math]x[/math] is 2.5?
An equilateral triangle has three sides of equal length.
Function [math]P[/math] gives the perimeter of an equilateral triangle of side length [math]s[/math].[br]Find [math]P\left(2\right)[/math].
Find [math]P\left(10\right)[/math].
Find [math]P\left(s\right)[/math].
Imagine a situation where a person is using a garden hose to fill a child's pool. Think of two quantities that are related in this situation and that can be seen as a function.
Define the function using a statement of the form “ [math]\underscore\underscore\underscore\underscore\underscore[/math]is a function of [math]\underscore\underscore\underscore\underscore\underscore[/math]. "[br]Be sure to consider the units of measurement.
Sketch a possible graph of the function. Be sure to label the axes.
Then, identify the coordinates of one point on the graph and explain its meaning.
Function [math]C[/math] gives the cost, in dollars, of buying [math]n[/math] apples. [br]Which statement best represents the meaning of [math]C\left(10\right)=9[/math]?
Diego is baking cookies for a fundraiser. He opens a 5-pound bag of flour and uses 1.5 pounds of flour to bake the cookies.
Which equation or inequality represents [math]f[/math], the amount of flour left in the bag after Diego bakes the cookies?