Functions and Their Intervals

Presentation

•

Mathematics

•

9th - 12th Grade

•

Medium

•

CCSS

6.NS.B.3, 8.EE.B.5, HSF.IF.A.2

Standards-aligned

Roderick Brannon

Used 8+ times

FREE Resource

3 Slides • 16 Questions

Multiple Choice

Find the slope of the line that passes through:
(6,7) and (4,2)

2/5

-5/2

5/2

-1/2

Multiple Choice

Find the slope

-5/3

-3/5

5/3

3/5

Multiple Select

Which three statements about the function are true?

g(1) = -1

g(0) = 0

g(4) = -2

g(1) = 1

g(-1) = 1

Multiple Select

Over what intervals is F(x) constant? Check all that apply.

$-10<x<-7$

$-7<x<-2$

$-2<x<-1$

$-1<x<4$

$4<x<8$

Multiple Select

Over what intervals is F(x) increasing? Check all that apply.

$-10<x<-7$

$-7<x<-2$

$-2<x<-1$

$-1<x<4$

$4<x<8$

Multiple Select

Over what intervals is F(x) decreasing? Check all that apply.

$-10<x<-7$

$-7<x<-2$

$-2<x<-1$

$-1<x<4$

$4<x<8$

Draw

Plot a point on the graph on an interval where the graph is increasing. Draw a line that touches the graph at that one point (tangent). How can we describe the slope of that line?

Draw

Plot a point on the graph on an interval where the graph is decreasing. Draw a line that touches the graph at that one point (tangent). How can we describe the slope of that line?

The point where the function changes from increasing to decreasing is another definition of a local minimum.
The point where the function changes from decreasing is another definition of a local minimum.

Draw

Plot a point on the graph where the function has a local max or min. Draw a line that touches the graph at that one point (tangent). How can we describe the slope of that line?

Multiple Choice

What is the relative maximum?

(1,0)

(2,2)

(0,-2)

(-2,8)

Multiple Choice

What is the relative minimum?

(1,2)

(2,2)

(0,-2)

(3.5, -11)

Multiple Choice

Identify where the function is decreasing.

x < -4 , x > 1

-4 < x < 1

-6 < x < 7.5

All Real Numbers

Multiple Choice

Identify the x-intercept(s) of the function.

$x=-2$

$x=-4$

$x=-4,-1$

$x=-4,-1,4$

Multiple Choice

Identify the y-intercept(s) of the function.

$y=-2$

$y=2,-2,\ -4.5$

$y=-4$

None

Multiple Choice

Over what interval is this function constant?

$x>-5$

$-3<x<4$

$x>4$

$-5$

Match

Match the following

When the graph is increasing....

When the graph is decreasing...

When the graph has a local max or min...

When the graph goes from increasing to decreasing...

When the graph goes from decreasing to increasing...

the tangent line slopes are positive

the tangent line slopes are negative.

the tangent line slopes is zero.

a local max has been reached.

a local min has been reached.

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