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Algebra 1

7.4.3 Comparing Exponential and Quadratic Functions

Algebra 17.4.3 Comparing Exponential and Quadratic Functions

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Activity

1.

Here are two functions: p(x)=6x2p(x)=6x2 and q(x)=3xq(x)=3x.

Investigate the output of pp and qq for different values of xx. For large enough values of xx, one function will have a greater value than the other.

Which function will have a greater value as xx increases?

Support your answer with tables, graphs, or other representations.

Are you ready for more?

Extending Your Thinking

1.

Janna says that some exponential functions grow more slowly than the quadratic function as xx increases. Do you agree with Janna? Be prepared to show your reasoning.

2.

Could you have an exponential function g(x)=bxg(x)=bx so that g(x)<f(x)g(x)<f(x) for all values of xx?

Video: Comparing Exponential and Quadratic Functions

Watch the following video to learn more about functions.

Self Check

Which of the following has the greatest value as x increases?
  1. y = ( 1 4 ) x
  2. y = 4 x
  3. y = 4 x
  4. y = 4 x 2

Additional Resources

Exponential versus Quadratic Functions

For each of the two functions, do the following:

  1. Complete the table of values.
  2. Sketch a graph.
  3. Decide whether each function is linear, quadratic, or exponential, and be prepared to explain how you know.
  1. f(x)=3·2xf(x)=3·2x
xx 11 00 11 22 33 55
f(x)f(x) 3232 or equivalent 33 66 1212 2424 9696
A graph of an exponential curve with plotted points. The x-axis ranges from -1 to 6 and the y-axis from 0 to 110. The curve rises slowly at first, then increases rapidly after x equals 3.

This function is exponential. It has a growth factor of 22.

  1. g(x)=3·x2g(x)=3·x2
xx 11 00 11 22 33 55
g(x)g(x) 33 00 33 1212 2727 7575
A graph of an quadratic curve with plotted points. The x-axis ranges from -1 to 6 and the y-axis from 0 to 110. The curve rises slowly at first, then increases after x equals 2.

This function is not linear because it does not have a constant rate of change, and it is not exponential because it does not have a constant growth factor. The function is quadratic because it can be represented by g(x)=3x2g(x)=3x2, which has xx to the second power, and that is the greatest power.

Note: Between f(x)f(x) and g(x)g(x), f(x)f(x) will have the greater value as xx increases.

Try it

Try It: Exponential versus Quadratic Functions

Which of the following has the greater value as xx increases, f(x)f(x) or g(x)g(x)?

f(x)=3x2f(x)=3x2

g(x)=3xg(x)=3x

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