Shahad practice

Drag and Drop

"Distance" represents Bill's distance from home. When was Bill furthest from home?

Placeholder

Drag these tiles and drop them in the correct blank above

5 seconds

1 second

2 seconds

4 seconds

Multiple Choice

"Distance" represents Bill's distance from home. When did Bill turn around to return home?

• 1 second

• 2 seconds

• 4 seconds

• 5 seconds

Multiple Choice

When was Bill not moving?

• Between 0 and 1 seconds

• Between 1 and 2 seconds

• Between 3 and 5 seconds

• Between 5 and 6 seconds

Multiple Choice

When is the ball at its maximum height?

• 1 second

• 2 seconds

• 3 seconds

• 4 seconds

Multiple Choice

When does the ball hit the ground?

• 1 second

• 2 seconds

• 3 seconds

• 4 seconds

Multiple Choice

Which of the following graphs best illustrates the relationship between the heat released by the foods listed in Table 1 and the change in water temperature?

• A

• B

• C

• D

Multiple Choice

How much does it cost to have your lawn mowed for 2 hours?

• $16
• $17
• $18
• $19

Multiple Choice

What is happening in the graph between 30 and 40 minutes?

• Sarah is accelerating
• Sarah is not moving
• Sarah is slowing down
• Sarah is travelling at a constant speed

Multiple Choice

• Taylor can write 6 words per minute

• Taylor can write 25 words per minute

• Taylor can write 50 words per minute

• Taylor can write 150 words per minute

Multiple Choice

• It is a function because each input has only one output.

• It's not a function because an input has multiple outputs.

• It's not a function because an output has multiple inputs.

• It is a function because each output has only one input.

Multiple Choice

• It is a function because each input is paired with only one output.

• It's not a function because inputs are paired with more than one output.

• It's not a function because outputs are paired with more than one input.

• It is a function because each output is paired with only one input.

Multiple Choice

• It is a function because each input is paired with only one output.

• It's not a function because inputs are paired with more than one output.

• It's not a function because outputs are paired with more than one input.

• It is a function because outputs are aired with only one input.

Multiple Choice

Approximately, which month did wheat export exceed rice export?

• June

• July

• August

• September

Multiple Choice

How long did one of the runner's rest?

• 8 seconds
• 13 seconds
• 5 seconds
• 50 seconds

Multiple Choice

What is happening at E?

• Stationary
• Accelerating
• Fast steady speed; moving away from the starting position
• Steady speed; returning to start position

Multiple Choice

Which runner had a head start?

• A
• B
• C

Multiple Choice

 Every morning, Tom walks along a straight road from his home to the bus stop. Below, is a graph representing Tom’s trip to school.
- What is the distance covered through the second segment, which is between 50 seconds, and 70 seconds?

• 40 meters
• 60 meters
• 80 meters
• 20 meters

Multiple Choice

Based upon the information in the table, predict the output value for an input of 30.

• 35

• 47

• 90

• 99

Multiple Choice

On which interval(s) is the given function increasing?

• (-∞, 2) U (-2, ∞)

• (-2, 2) U (-2, ∞)

• (-∞, -2) U (0.5, ∞)

• (0, 2) U (0.5, ∞)

Multiple Choice

Identify the interval from the graph where the function is concave down

• (-1,1) & (3,4)

• (-2,4)

• (-3,-1) & (1,3)

• (-2,1) & (1,4)

Change in
Tandem

Change in Tandem

Use of Graphs.....

• Graphs track how two quantities change together or change in tandem => rate of change.

• A graph can be described using x-intercepts & y-intercepts, intervals over which the function is increasing and decreasing, and maximum and minimum points.

• output

• range

• dependent

y-axis

• input

• domain

• independent

x-axis

Remember.......

​x

​x

​

​(x, y)

Multiple Choice

Rate of change describes how two quantities change together?

• TRUE

• FALSE

Multiple Select

Check all that are used to describe dependent:

• range

• y-axis

• output

• domain

• x-axis

Concavity =>

​Concave Up
Concave Down

​Concave Up

​Concave Down

Concave Up =>"make a cup"

A graph is concave up, if for equal changes in the input, the corresponding change in output is increasing.

​Rate of change
is increasing

​Graph
Increasing

​Graph
Decreasing

​Doesn't matter if the graph is increasing or decreasing, the rate of change is increasing.

Concave Down =>"make a frown"

A graph is concave down, if for equal changes in the input, the corresponding change in output is decreasing.

​Rate of change
is decreasing

​Graph
Increasing

​Graph
Decreasing

​Doesn't matter if the graph is increasing or decreasing, the rate of change is decreasing.

Multiple Select

Check all that apply for: Concave Up

• Rate of change: increasing

• equal change in the input, increasing change in output

• equal change in the input, decreasing change in output

Multiple Choice

Equal changes in the input result in decreasing changes in the output.

• Concave Up

• Concave Down

Multiple Choice

The table describes the change of a function f for selected intervals of x. The function f is defined for 0 ≤ x ≤4. On which of the following intervals is the graph concave up.

• 0 < x < 1

• 1 < x < 2

• 2 < x < 3

• 3 < x < 4

Multiple Select

​A ball is thrown through an open window to the ground below. The height of the ball, in meters, at time t seconds after it is thrown can be modeled by the function ℎ, given by ℎ(t) = -4.9t² + 4.4t + 15.24. Check all that apply to this scenario

• Concave down

• Concave up

Multiple Choice

Find the slope of

$$\left(-1,3\right)\ and\ \left(2,5\right)$$  

• $$\frac{2}{3}$$  

• $$\frac{3}{2}$$  

• $$-\frac{2}{3}$$  

• $$-\frac{3}{2}$$  

Multiple Choice

What is the rate of change of

$$\left(-3,7\right)\ and\ \left(5,-9\right)$$  

• $$-2$$  

• $$2$$  

• $$-\frac{1}{2}$$  

• $$\frac{1}{2}$$  

Multiple Choice

What is the slope of

$$\left(2,6\right)\ and\ \left(7,\ 21\right)$$  

• $$3$$  

• $$-3$$  

• $$\frac{1}{3}$$  

• $$\frac{1}{2}$$  

Multiple Choice

What is the rate of change of

$$\left(4,6\right)\ and\ \left(7,9\right)$$  

• $$1$$  

• $$3$$  

• $$-1$$  

• $$-3$$  

Multiple Choice

What is the rate of change?

• $$5$$

• $$-5$$

• $$\frac{1}{5}$$

• $$-\frac{1}{5}$$

Multiple Choice

What is the y-intercept?

• (0,7)

• (0,0)

• (0,1)

• (0,2)

Remember, if a relation is a function, then every input has exactly one output.

​

If a graph passes the vertical line test it is a function.​

​

​Functions

​

Multiple Choice

Which of the following relations is a function?

• a.)

• b.)

Multiple Choice

Which of the following graphs represents y as a function of x?

If a function is even, opposite inputs give you the same output.

f(-x) = f(x)​

​

Also, if a function is even, it's graph is symmetric about the y-axis.​

​

​Some text here about the topic of discussion.

​Even Functions

​

Multiple Choice

If a function is even and contains the point (4, -7), what other point is guaranteed to be on the graph?

Use the fact that f(-x)=f(x)

• (-4, 7)

• (-7, 4)

• (-4, -7)

• (4, 7)

Multiple Choice

Is the following function even?

• Yes

• No

Multiple Choice

Is the following function even?

• Yes

• No

If a function is odd, opposite inputs give you opposite outputs.

f(-x) = -f(x)​

​

Also, if a function is even, it's graph is symmetric about the origin.​

​

​Some text here about the topic of discussion.

​Odd Functions

​

Multiple Choice

If a function is odd and contains the point (4, -7), what other point is guaranteed to be on the graph?

Use the fact that f(-x) = -f(x)

• (-4, 7)

• (-7, 4)

• (-4, -7)

• (4, 7)

Multiple Choice

Is the following function odd?

• Yes

• No

Multiple Choice

Is the following function odd?

• Yes

• No

If a function is one-to-one, then it has an inverse.

​

To prove a function is one-to-one, use the horizontal line test.​

​

​Some text here about the topic of discussion.

​One-to-One

​

​Does not pass the horizontal line test

Multiple Choice

Is the following function one-to-one?

• Yes

• No

Multiple Choice

Is the following function one-to-one?

• Yes

• No

Match

Match the following:

• If a function is odd, then opposite inputs = ...

• If a function is odd, it's graph is symmetric about the ...

• If a function is even, then opposite inputs = ...

• If a function is even, then opposite inputs = ...

opposite outputs

origin

same outputs

same outputs

• opposite outputs

• origin

• same outputs

• same outputs

Match

Match the following:

• If a graph is a function, it will pass the ...

• To determine if a function has an inverse, it must pass the ...

• ---

vertical line test

horizontal line test

---

• vertical line test

• horizontal line test

• ---

To find the inverse of a function, you should:​

​

1.) replace f(x) with y

2.) interchange x and y

3.) solve for y​

​

​

​

​Some text here about the topic of discussion.

​Inverse Functions

​

Reorder

Reorder the steps when finding the inverse to the function: $$f\left(x\right)=3x-4$$  

• $$y=3x-4$$  

• $$x=3y-4$$  

• $$x+4=3y$$  

• $$\frac{x+4}{3}=y$$  

• $$f^{-1}\left(x\right)=\frac{x+4}{3}$$  

1

2

3

4

5

• 1
• 2
• 3
• 4
• 5

Multiple Choice

Find the inverse to the following function:

(you might need to open a scratch pad for this) $$f\left(x\right)=2\sqrt[]{x-5}$$  

• $$f^{-1}\left(x\right)=\frac{\left(x+5\right)^2}{2}$$  

• $$f^{-1}\left(x\right)=\frac{x^2}{4}+5$$  

• $$f^{-1}\left(x\right)=2x^2+5$$  

• $$f^{-1}\left(x\right)=\frac{x^2}{2}+5$$  

Multiple Choice

If h(x) contains the point (4,-7), what point is guaranteed to be on the inverse function h^-1(x)?

• (-4, 7)

• (-7, 4)

• (-4, -7)

• (4, 7)

​Inverse Functions

​To prove f(x) and g(x) are inverse, you can...

1.) graph them and show that they are symmetric about the line y = x

​

2.) show that f(g(x)) = g(f(x)) = x​

Some text here about the topic of discussion

Draw

Show that f(x) and g(x) are inverses by graphing.

$$f\left(x\right)=3x-3$$  

$$g\left(x\right)=\frac{x+3}{3}$$  

Draw

Show that f(x) and g(x) are inverses algebraically. (Show f(g(x)) = g(f(x)) = x

$$f\left(x\right)=3x-3$$  

$$g\left(x\right)=\frac{x+3}{3}$$  

Multiple Choice

What is the value of f(-3)?

• 0

• -2

• -4

• 3

Multiple Choice

What is the value of f(0)?

• 0

• -2

• -4

• 3

Multiple Choice

What is the value of f(3)?

• 0

• -2

• -4

• 3

Multiple Choice

For what value of x does f(x)=0?

• x = 1

• x = 2

• x = 3

• x = 4

Multiple Choice

The graph of the function f is given for $$-3\le x\le6$$ .

Which of the following statements must be true about the rate of change of f over the interval $$-3<x<2$$ ?

• The rate of change is positive.

• The rate of change is negative.

• The rate of change is increasing.

• The rate of change is decreasing.

Multiple Choice

The table gives characteristics of the rates of change of the function f on different intervals. Which of the following is true about f on the interval $$3<x<4$$ ?

• f is increasing, and the graph of f is concave down

• f is increasing, and the graph of f is concave up

• f is decreasing, and the graph of f is concave down

• f is decreasing, and the graph of f is concave up

Multiple Choice

Slope is know as rise/

• run
• fall
• none
• rise

Multiple Choice

Find the slope of the line.

• Undefined
• 0
• 1
• -1

Multiple Choice

Find the average rate of change over the given interval. 

• 4
• 7
• 7/3
• 3/7