Unit 1 Review Lesson: Functions

Presentation

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Mathematics

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9th - 12th Grade

•

Practice Problem

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Medium

•

CCSS

HSF-IF.C.7A, HSF.IF.A.2, 8.F.A.1

Standards-aligned

Kevin Johnson

Used 69+ times

FREE Resource

14 Slides • 22 Questions

Unit 1 Review:

Functions

Review Content

Notations
Domain and Range
Intervals of Increase and Decrease
Maximums and Minimums
Evaluation
Zeros and x intercepts
End Behavior

Notation forms

Inequality on the first column and Interval on the last column.

Forms

Inequalities use < and > symbols
Intervals use ( ) and [ ]

Joining two intevals

union notation

Multiple Choice

Express the following in Interval Notation

-8 ≤ x < 8

[-8, 8]

[-8,8)

(-8, 8]

(-8, 8)

Multiple Choice

Express the following interval in Set notation:

[3, 5]

3 ≤ x ≤ 5

3 < x ≤ 5

3 ≤ x < 5

3 < x < 5

Multiple Choice

Look at the graph. Write the inequality in interval notation.

(-2,5)

(-∞,-2)⋃(5,∞)

[-2,5]

(-∞,-2]∪[5,∞)

Domain and Range

Multiple Choice

What is the domain of a relation?

the set of all y-values

the set of all x-values

Multiple Choice

For the function {(0,1), (1,-3), (2,-4), (-4,1)}, write the domain and range.

D: {1, -3, -4,}

R: {0, 1, 2, -4}

D:{0, 1, 2, -4}

R:{1, -3, -4}

D:{0, 1, 2, 3, 4}

R:{1, -3, -4}

Multiple Choice

What is the range of the graph?

Remember: Range is y!

-7 ≤ x < 5

-3 ≤ x < 1

-3 ≤ y < 1

-7 ≤ y < 5

Multiple Choice

What is the range of the function?

[-1, +∞)

(-1,1)

[1.5, +∞)

(-2, 2)

Intervals of increase and decrease

What are intervals of increase and decrease?

Intervals of increase and decrease are the domain of a function where its value is getting larger or smaller, respectively.

Multiple Choice

Where is the function decreasing?

(-∞, -1)

(-∞, 3)

(-1, ∞)

(-∞, ∞)

Multiple Choice

When is this function increasing?

-3<x<3

x>2.5

-2.5<x<2.5

x>3

Multiple Choice

Describe the interval(s) over which the given function is decreasing.

(-∞, 0) U (2, ∞)

(5, -4) U (0, -3)

(2, 3)

(-3, 0) U (2, 3)

Local Maximums and Minimums

Maximum at the top of curve. Minimum at bottom of curve.

Multiple Choice

What is the green dot on the parabola called?

minimum

zero

maximum

root

Multiple Choice

What is the relative maximum?

(1,2)

(2,2)

(0,-2)

Multiple Select

Identify all local minimums.

(3.25, 2.25)

(2.25, 4.5)

(−.5, −7.5)

(5,6)

Evaluation

Substitute for x then use PEMDAS

Multiple Choice

Evaluate f(x) = 3x - 4 when f(3)

Multiple Choice

Evaluate f(x) = 6(x - 3) when f(-3)

-36

Multiple Choice

For the function: f(x) = 7(x - 11), f (16) = _____

Zeros and x intercepts

Both are found where the graph crosses or touches the x axis.
zero: x = #
x intercept: (x , 0)

Multiple Choice

How many zeroes are shown in the graph?

Multiple Choice

What are all the x-intercepts?

(-2.55, 0), (2.55, 0)

(0, 36)

(-3,0), (-2,0), (2,0), (3,0)

(-∞,∞)

Multiple Choice

What are the zeros?

There are none

x = - 4

x = - 3.5 and 3.5

x = - 1.5 & 1.5

End Behavior

Describes where y values are approaching as x values move left and right toward infinities
"As x approaches infinity, f(x) approaches ____"
"As x approaches negative infinity, f(x) approaches ____"

Multiple Choice

What is the End behavior on the left side?

As x →-∞, f(x) →∞

As x →∞, f(x) →-∞

As x →∞, f(x) →∞

As x →-∞, f(x) →-∞

Multiple Choice

As x⟶∞, f(x)⟶...

$-\infty$

$\infty$

Multiple Choice

Which of the following indicates that as x moves left you moves up?

As f(x)⟶∞, f(x)⟶∞

As x ⟶−∞, f(x)⟶−∞

As x⟶−∞, f(x)⟶∞

Unit 1 Review:

Functions

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