Input in, output out
A polynomial as a function
A number machine
A machine uses the rule 2x + 3. You put a number in, the machine puts it in place of x and gives a number back. You feed in x = 4.
What do you think comes out?
What this lesson covers
The idea
A polynomial acts as an input-output process: substituting a value of x (input) gives the value of the polynomial (output), so the expression is a function of x, such as a linear or quadratic function.
A number machine
A machine uses the rule 2x + 3. You put a number in, the machine puts it in place of x and gives a number back. You feed in x = 4.
What do you think comes out?
- 11
- 9
- 24
Run the machine
Feed numbers in with the slider or the + and − buttons. The machine puts your number in place of x.
A function of x
A polynomial acts as an input-output process: put in a value of x (the input) and the value of the polynomial comes out (the output). So the expression is a function of x, such as a linear function or a quadratic function.
2x + 3 is a linear function. 10x − x² is a quadratic function. Input 3 gives 10 × 3 − 3² = 21.
Notes
A polynomial is an input-output process: the input is x, the output is the value of the polynomial. The expression is a function of x.
Check yourself
The machine is 2x + 3. What is the output when the input is 5?
Answer: 13
2 × 5 + 3 = 10 + 3 = 13.
The machine is 2x + 3. What is the output when the input is −4?
Answer: -5
2 × (−4) + 3 = −8 + 3 = −5.
10x − x² is a…
The machine is 10x − x². What is the output when the input is 4?
Answer: 24
10 × 4 − 4² = 40 − 16 = 24.
- quadratic function — correct. Yes. Its highest power is 2.
- linear function. It has x², so its degree is 2, not 1.
- cubic function. The highest power is 2, not 3.