Unit 1 Review Lesson: Functions

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)

• 5

• 13

• 2

• 4

Multiple Choice

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

• 0

• 36

• -36

Multiple Choice

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

• 5

• 16

• 35

• 28

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?

• 1

• 2

• 3

• 4

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)⟶∞