Comparing Functions Part 3

Presentation

•

Mathematics

•

9th Grade

•

Practice Problem

•

Medium

•

CCSS

6.NS.B.3, 8.F.A.2, HSF-LE.A.1B

Standards-aligned

Raymee Burrell

Used 4+ times

FREE Resource

17 Slides • 32 Questions

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.

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)?

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.

f(x) = 2x

g(x) = x² h(x) = 2^x

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.

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.

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)

m(x)

w(x)

p(x)

-3

-2

f(x)

-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

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

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

Reorder

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

Exponential Function

Quadratic Function

Linear Function

Reorder

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

Exponential Function

Linear Function

Quadratic Function

Reorder

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

Quadratic Function

Linear Function

Exponential Function

Fill in the Blanks

Fill in the Blanks

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

Comparing
Functions

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