Functions and Their Intervals

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.

• 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.