Functions and Relations Question
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Grade 11 Functions and Relations CCSS: HSF-LE.A.3
The following table gives some of the values of f(x), a quadratic function, and g(x), an exponential function. What can be concluded from these values (and general properties of the functions), and why?
| x | f(x) | g(x) |
| 8 | 32.0 | 1.5 |
| 9 | 40.5 | 4.1 |
| 10 | 50.0 | 11.0 |
| 11 | 60.5 | 29.9 |
| 12 | 72.0 | 81.4 |
| 13 | 84.5 | 221.2 |
- g(x)>f(x) for 12≤x≤20. f(x) is quadratic and has a minimum near x=16, as is indicated by the values in the table. After this point, f(x) will start growing more rapidly than g(x) and become greater than g(x) for x>20.
- g(x)>f(x) for x≥12. Since exponential functions and quadratic functions can only intersect at one point, the intersection point near x=11.5 means that g(x)>f(x) for x≥12 and f(x)>g(x) for x≤11.
- g(x)>f(x) for all values of x. Since g(x) is exponential, it must therefore always be greater than a quadratic function.
- g(x)>f(x) for x≥12. Since g(x) is exponential, the difference of values between each unit interval will continue to increase. Although the difference of quadratic values will also increase, they do so at a much slower rate.