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9-12 Extra Support Materials for Algebra 1 Unit 6 Lesson 23

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Extra Support Materials for Algebra 1

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Lesson 23

23.1 Warm-up 23.2 Activity 23.3 Activity

Unit 6, Lesson 23

Evaluating Functions over Equal Intervals

Extra Support Materials for Algebra 1

23.1

Warm-up

Find the slope of each line.
1. The line that passes through and .
2. The graph of .
Show on each graph where the slope can be seen.

<p>2 comma 2 and 3 comma 6 on a graph of a line </p>

<p>Graph of line f. y intercept = -2. Slope = the fraction 1 over 3.</p>

23.2

Activity

Standards Alignment

Building On

Addressing

F-IF.2

Use function notation, evaluate functions for inputs in their domains, and interpret statements that use function notation in terms of a context.

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Building Toward

F-LE.1.a

Prove that linear functions grow by equal differences over equal intervals, and that exponential functions grow by equal factors over equal intervals.

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For the function , evaluate:
1. and
2. and
3. and
4. and
What do all those pairs of numbers you found have in common?
Write an expression for and .
What would you expect to be the result of subtracting from ?
Subtract from . If you don’t get the answer you predicted, work with a partner to check your algebra.
For the function , evaluate:
1. and
2. and
3. and
4. and
What do all those pairs of numbers you found have in common?
Write an expression for and .
What would you expect to be the result of dividing by ?
Divide by . If you don’t get the answer you predicted, work with a partner to check your algebra.

23.3

Activity

Standards Alignment

Building On

Addressing

8.EE.1

Know and apply the properties of integer exponents to generate equivalent numerical expressions. For example, 3² × 3^-5 = 3^-3 = 1/3³ = 1/27.

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Building Toward

F-LE.1.a

Prove that linear functions grow by equal differences over equal intervals, and that exponential functions grow by equal factors over equal intervals.

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Evaluate:
Solve for :
Write an equivalent expression using as few terms as possible:

None

Standards Alignment

Building On

8.EE.6

Use similar triangles to explain why the slope m is the same between any two distinct points on a non-vertical line in the coordinate plane; derive the equation y = mx for a line through the origin and the equation y = mx + b for a line intercepting the vertical axis at b.

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8.F.4

Construct a function to model a linear relationship between two quantities. Determine the rate of change and initial value of the function from a description of a relationship or from two (x, y) values, including reading these from a table or from a graph. Interpret the rate of change and initial value of a linear function in terms of the situation it models, and in terms of its graph or a table of values.

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Addressing

Building Toward