IXL - Compare linear, exponential, and quadratic growth (Algebra 1 practice)

Complete the table of values for

(

)

and

(

)

x	f ( x )	g ( x )
0
1
2
3

Both

(

)

and

(

)

grow as x gets larger and larger. Which function eventually exceeds the other?

(

)

(

)

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Learn with an example

question

Complete the table of values for

(

)

and

(

)

x	f ( x )	g ( x )
1
2
3
4

Both

(

)

and

(

)

grow as x gets larger and larger. Which function eventually exceeds the other?

(

)

(

)

solution

First, complete the table. Plug the

x-values

into

(

)

and

(

)

Start by plugging

into

(

)

(

)

(

)

(

)

Next, plug

into

(

)

(

)

(

)

Use the identity

Find the rest of the missing values in the same way.

x	f ( x )	g ( x )
1	5	3
2	7	5
3	9	9
4	11	17

Now, notice that

(

)

is greater than

(

)

when x is 1 or 2 and that

(

)

is equal to

(

)

when x is 3. When x is 4, however,

(

)

is greater than

(

)

x	f ( x )	g ( x )
1	5	3
2	7	5
3	9	9
4	11	17

If you evaluate

(

)

and

(

)

for larger and larger values of

(

)

will continue to be greater than

(

)

In other words,

(

)

exceeds

(

)

for all values of x greater than 3.

Notice that

(

)

is a linear function and that

(

)

is an exponential function. Functions that grow exponentially always exceed functions that grow linearly for large enough values of

You can also see that

(

)

eventually exceeds

(

)

by comparing their graphs. Once x gets large enough, the graph of

(

)

is above the graph of

(

)

Looking for more? Try these:

Lesson: Linear functions

Lesson: Exponential growth

Lesson: Quadratic functions

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Teacher tools

Work it out

Not feeling ready yet? These can help:

AA.11Compare linear and exponential growth

AA.2Identify linear, quadratic, and exponential functions from graphs

Lesson: Linear functions

Lesson: Exponential growth

Lesson: Quadratic functions

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