1.2 Characteristics of Function Graphs (Due 10/1/24)

Essential Question: What are some of the attributes of a function, and how are they related to the function’s graph?

Learning Target: Students will be able to describe the key features of the graphs of functions and use the graphs to make predictions about the data.

Show your work for full credit.

Required

10

Use the graph to create a function with the following features:

1) As x gets smaller; the function gets larger. x→ - ∞; f(x)→ ∞
2) As x gets larger; the function gets larger. x→ ∞; f(x)→ ∞
3) The graph of the function passes through the x-axis at -3.

Required

10

Use the graph to create a function with the following features:

1) As x gets smaller; the function get larger. x→ - ∞; f(x)→ ∞
2) As x gets larger; the function get smaller. x→ ∞; f(x)→ - ∞
3) The graph of the function passes through the x-axis at -3.
4) The graph of the function passes through the x-axis at 0.

Finding the Characteristics of Functions

Required

28

Required

28

Fill in the blanks for the attributes of the functions shown in the graph.

f (x) is positive on the interval=_______ (If none write none)
f (x) is negative on the interval=_______ (If none write none)
f (x) has a zero at =_______ 
f(x) is increasing on the interval=_______ (If none write none)
f (x) is decreasing on the interval=_______ (If none write none)
f (x) has a local minimum of f(x)=_______ at x= _______ (If none write none)
f (x) has a local minimum of f(x)=_______ at  x=_______ (If none write none)

Required

36

Fill in the blanks for the attributes of the functions shown in the graph.

f (x) is positive on the interval=_______   (If none write none)
f (x) is negative on the interval=_______  (If none write none)
f (x) has a zero(s) at x =_______   (If none write none)
f(x) is increasing on the interval=_______   (If none write none)
f (x) is decreasing on the interval=_______   (If none write none)
f (x) has a local minimum of f(x)=_______ at x= _______   (If none write none)
f (x) has a local maximum of f(x)=_______ at x=_______   (If none write none)

Required

40

Fill in the blanks for the attributes of the functions shown in the graph.

f (x) is positive on the interval=_______ (If none write none)
f (x) is negative on the interval=_______ (If none write none)
f (x) has a zero(s) at =_______ and _______ 
f(x) is increasing on the interval=_______ (If none write none)
f (x) is decreasing on the interval=_______ (If none write none)
f (x) has a local minimum of f(x)=_______ at  x=_______ (If none write none)
f (x) has a local maximum of f(x)=_______ at  x=_______ (If none write none)

Required

40

Fill in the blanks for the attributes of the functions shown in the graph.

f (x) is positive on the interval=_______  (If none write none)
f (x) is negative on the interval=_______ (If none write none)
f (x) has a zero(s) at =_______ and _______ 
f(x) is increasing on the interval=_______ (If none write none)
f (x) is decreasing on the interval=_______ (If none write none)
f (x) has a local minimum of f(x)=_______ at  x=_______ (If none write none)
f (x) has a local maximum of f(x)=_______  at  x=_______ (If none write none)

Spiral Review

Required

5

For what interval of x is the function f(x) increasing?

Required

5

For what interval of x is the function f(x) decreasing?

Required

5

Identify one interval of (x) where the function f(x) positive.

Required

5

Identify one interval of time (x) where the function f(x) decreasing.

Required

5

Identify one interval of time (x) where the function f(x) increasing.

5

Identify the intervals of x where the function f(x) increasing.
_______ U_______ 

Required

5

For what interval of x is the function f(x) decreasing?

Required

5

Find the missing value of c.

Required

4

Is this an open or closed interval?

5

Use interval notation to describe the domain of this function.

Required

10

Simplify. Your answer should not have negative exponents.

Learning Log

Required

5

Required

5

Required

10

1.2 Characteristics of Function Graphs (Due 10/1/24)

Essential Question: What are some of the attributes of a function, and how are they related to the function’s graph?

Learning Target: Students will be able to describe the key features of the graphs of functions and use the graphs to make predictions about the data.

Show your work for full credit.

Use the graph to create a function with the following features:1) As x gets smaller; the function gets larger. x→ - ∞; f(x)→ ∞2) As x gets larger; the function gets larger. x→ ∞; f(x)→ ∞3) The graph of the function passes through the x-axis at -3.

Finding the Characteristics of Functions

Spiral Review

For what interval of x is the function f(x) increasing?

For what interval of x is the function f(x) decreasing?

Identify one interval of (x) where the function f(x) positive.

Identify one interval of time (x) where the function f(x) decreasing.

Identify one interval of time (x) where the function f(x) increasing.

For what interval of x is the function f(x) decreasing?

Find the missing value of c.

Is this an open or closed interval?

Use interval notation to describe the domain of this function.

Simplify. Your answer should not have negative exponents.

Learning Log

Essential Question: What are some of the attributes of a function, and how are they related to the function’s graph?

Learning Target: Students will be able to describe the key features of the graphs of functions and use the graphs to make predictions about the data.

Show your work for full credit.

Use the graph to create a function with the following features:1) As x gets smaller; the function gets larger. x→ - ∞; f(x)→ ∞2) As x gets larger; the function gets larger. x→ ∞; f(x)→ ∞3) The graph of the function passes through the x-axis at -3.

Finding the Characteristics of Functions

Spiral Review

For what interval of x is the function f(x) increasing?

For what interval of x is the function f(x) decreasing?

Identify one interval of (x) where the function f(x) positive.

Identify one interval of time (x) where the function f(x) decreasing.

Identify one interval of time (x) where the function f(x) increasing.

For what interval of x is the function f(x) decreasing?

Find the missing value of c.

Is this an open or closed interval?

Use interval notation to describe the domain of this function.

Simplify. Your answer should not have negative exponents.

Learning Log

Use the graph to create a function with the following features:

1) As x gets smaller; the function gets larger. x→ - ∞; f(x)→ ∞
2) As x gets larger; the function gets larger. x→ ∞; f(x)→ ∞
3) The graph of the function passes through the x-axis at -3.

Use the graph to create a function with the following features:

1) As x gets smaller; the function gets larger. x→ - ∞; f(x)→ ∞
2) As x gets larger; the function gets larger. x→ ∞; f(x)→ ∞
3) The graph of the function passes through the x-axis at -3.