Comparing Functions Part 3

Comparing
Functions

Consider the following functions; fill in the blank comparing the
functions with an inequality symbol.

a. f(x) = -x² - 3
g(x) = ½x – 2
 

For all values of x,

f(x) _ g(x)

​https://www.desmos.com/testing/georgia/graphing

Multiple Choice

Consider the following functions; fill in the blank comparing the functions with an inequality symbol.

p(x) = 3^x + 2

q(x) = ½x – 2

For all values of x,

p(x) _____ q(x)

• $$<$$

• $$>$$

• $$=$$

Consider the following graphed functions; fill in the blank
comparing the functions with an inequality symbol.

a.

For all values of x,

g(x) _f(x)

​​https://www.desmos.com/testing/georgia/graphing

Multiple Choice

Consider the following functions; fill in the blank comparing the functions with an inequality symbol.

For all values of x,

h(x) _____ k(x)

• $$<$$

• $$>$$

• $$=$$

For which values of x is f(x) > g(x)?

1.

Multiple Select

For which values of x is f(x) > g(x)?

Maybe More Than One Answer

• $$\left(-\infty,\ 1\right)$$

• $$\left(\ 1,\ 4\right)$$

• $$\left(4,\ \infty\right)$$

Multiple Select

For which values of x is f(x) > g(x)?

Maybe More Than One Answer

• $$\left(-\infty,\ 0\right)$$

• $$\left(\ 0,\ 2\right)$$

• $$\left(2,\ \infty\right)$$

For the following functions, use DESMOS to create a table and graph each function in a different color.

x

f(x) = 2x

g(x) = x² h(x) = 2^x

0

1

2

3

4

5

​https://www.desmos.com/testing/georgia/graphing

For the following functions, use DESMOS to create a table and graph each function in a different color.

For the following functions, use DESMOS to create a table and graph each function in a different color.

a) Which function shows a constant rate of change in its
y values? How is this displayed on your graph?

​​A. f(x) = 2x

B. g(x) = x²

C. h(x) = 2^x

Multiple Choice

Which function is largest  between 1 < x < 2?

• f(x) = 2x

• h(x) = 2^x

• g(x) = x²

Multiple Choice

How is this displayed on your graph?

• Line

• Curve

• U - Shaped

Multiple Choice

Eventually, which type of function shows the most rapid rate of growth in its y values?

• f(x) = 2x

• h(x) = 2^x

• g(x) = x²

Multiple Choice

How is this displayed on your graph?

• Line

• Curve

• U - Shaped

Consider the following functions.

a.

f(x) = -(½)^x

g(x) = - 1.5x + 3

A. f(x)

B. g(x)

Multiple Choice

Consider the following functions.

As $$x\ \longrightarrow\ \infty$$   , which function becomes the largest?

• f(x)

• g(x)

Multiple Choice

Consider the following functions.

As $$x\ \longrightarrow\ \infty$$   , which function becomes the largest?

• f(x)

• g(x)

x

0

1

2

3

4

5

m(x)

1

2

3

4

5

6

x

0

1

2

3

4

5

w(x)

2

3

6

11

18

27

1

2

3

4

5

1

5

13

29

x

0

1

2

3

4

5

p(x)

-3

-2

1

6

13

22

f(x)

x

0

-2

-1

Multiple Choice

A partial set of values is provided for two functions in each problem below. For all $$x\ge0$$  , which function would most likely be greater. If the greater function changes determine the appropriate intervals.

• g(x)

• h(x)

Multiple Choice

A partial set of values is provided for two functions in each problem below. For all $$x\ge0$$  , which function would most likely be greater. If the greater function changes determine the appropriate intervals.

• f(x)

• p(x)

Multiple Choice

Consider the function and given the transformation determine which statements are true and which are false.

– f(x) < g(x) for all values of x.

• True

• False

Consider the function and given the transformation determine which statements are true and which are false.

a. p(x) < h(x) + 3 for all
values of x.

b. p(x) < h(x – 3) for all
values of x.

c. p(x – 4) < h(x) for all
values of x.

Multiple Choice

Consider the function and given the transformation determine which statements are true and which are false.

f(–x) < g(x) for all values of x.

• True

• False

Multiple Choice

Consider the function and given the transformation determine which statements are true and which are false.

f(x) > – g(x) for all values of x.

• True

• False

Match

Match the following function name to the letter.

• Linear Function

• Quadratic Function

• Exponential Function

A

B

C

• A

• B

• C

Multiple Choice

Which function has the largest x-intercept?

• Linear Function

• Quadratic Function

• Exponential Function

Multiple Choice

Which function has the largest y-intercept?

• Linear Function

• Quadratic Function

• Exponential Function

Multiple Choice

Which functions have a positive rate of change throughout the entire graph?

• Linear Function

• Quadratic Function

• Exponential Function

Multiple Choice

Which functions have a negative rate of change throughout the entire graph?

• Linear Function

• Quadratic Function

• Exponential Function

Multiple Choice

Which functions has a rate of change that is negative and positive?

• Linear Function

• Quadratic Function

• Exponential Function

List the functions in order from smallest to biggest when x = -1:

Reorder

List the functions in order from smallest to biggest when x = 0:

• Quadratic Function

• Exponential Function

• Linear Function

1

2

3

• 1
• 2
• 3

Reorder

List the functions in order from smallest to biggest when x = 3:

• Exponential Function

• Quadratic Function

• Linear Function

1

2

3

• 1
• 2
• 3

Reorder

List the functions in order from smallest to biggest when x = 6:

• Exponential Function

• Linear Function

• Quadratic Function

1

2

3

• 1
• 2
• 3

Reorder

List the functions in order from smallest to biggest when x = 9:

• Quadratic Function

• Linear Function

• Exponential Function

1

2

3

• 1
• 2
• 3

Fill in the Blanks

At what two x's values does the Exponential and Quadratic Function intersect?

Fill in the Blanks

At what x value does the Linear and Quadratic Function intersect?

Fill in the Blanks

At what x value does all the Function intersect?

k. Which function has the largest
Average Rate Of Change from [2, 4]?

l. Which function has the largest
Average Rate Of Change from [5, 7]?

Multiple Choice

Which function has the largest Average Rate Of Change

from [2, 4]?

• Linear Function

• Quadratic Function

• Exponential Function

Multiple Choice

Which function has the largest Average Rate Of Change

from [5, 7]?

• Linear Function

• Quadratic Function

• Exponential Function

Multiple Choice

Which function has the largest Average Rate Of Change

from [4, 6]?

• Linear Function

• Quadratic Function

• Exponential Function

Multiple Choice

Which function has the largest Average Rate Of Change

from [7, 8]?

• Linear Function

• Quadratic Function

• Exponential Function

TOD: Comparing Functions - Week 8 Participation