CCSS.Math.Content.8.F.A.2:  Comparing two Functions

Math-8th GradeBrent Buckley

2-18-2012

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Function- Equation where each input has exactly one output.

Functions can be represented four ways:◦ Algebraically

Ex. Y=2X+3◦ Graphically◦ Numerically◦ Verbally

There are three more outputs than two inputs.

Quick Review

X Y

1 5

2 7

3 9

Given two functions, f(x)=3x+1 and g(x)=(1/3)x+1, which is a more dramatic rate of change?

F(x)=3x+1 is greater because 3 is a stronger multiplier than 1/3 is.

Comparisons can be made in any of the four representations.

Same Format Comparisons

X f(x) g(x)

1 4 4/3

2 7 5/3

3 10 2 or 6/3

If we know how to compare functions in any format given, than we will be able to compare two functions given in different formats.

Y=2x+5 The output is three more than the input

negative four times. These can be compared by making them

into the same format of function. (continued on next slide)

Comparisons in Different Formats

We can take the verbal function and translate it into an algebraic format to compare.

The output (y) is three more (+3) than the input negative four times (-4x)

Putting it together we have y=-4x+3 to compare to y=2x+5

This shows that these functions contain opposite slopes with the -4x descending twice as fast as the 2x.

A website for review this lesson

Ex. 1(Continued)

Question 1◦ How many outputs does each input in a function

have?

Time for a review!

Answer A

Answer B

Each input in a function has only one output!

Correct!

Next Question

A function has only one output for every input.

Try again.

Next Question

Question 2◦ Which function has the greater rate of change?

Time for a review!

x F(x) G(x)

1 4 2 ½

2 7 3

3 10 3 ½

F(x) G(x)

F(x) has the greater rate of change. You can see this by looking at the outputs for the f(x) column.

Correct!

Next Question

G(x) has the smallest rate of change between the two. Look at the difference between the numbers in the table.

Incorrect!

Next Question

Question 3:◦ Using what we learned, which one of these

functions, written in different formats, has the greater rate of change? The output is two less than three of the input.(f(x))

Time for a review!

x G(x)

1 3

2 5

3 7

F(x) has the greater rate of change. You can see this by translating the two functions to a common format.

Correct!

sources

G(x) has the smallest rate of change between the two. You can find this by translating the two functions to a common format and comparing them.

Incorrect!

sources

http://www.mathsisfun.com/definitions/function.html

http://www.corestandards.org/Math/Content/8/F/A/2

http://faculty.up.edu/wootton/Calc1/Section1.1.pdf

sources