We are building a library of Elementary Functions.
We will use our library of functions quite often as our reason for conclusions within our analysis.
We have our first two library entries.
Linear functions are functions which CAN be described with a formula of the form
where \(A\) and \(B\) are real numbers.
- \(A\) is called the leading coefficient
- \(A \, t\) is called the linear term
- \(B\) is called the constant term
Quadratic functions are functions which CAN be described with a formula of the form
where \(A\), \(B\), and \(C\) (called coefficients) are real numbers with \(A \ne 0\)
- \(A\) is called the leading coefficient
- \(A \, t^2\) is called the leading or quadratic term
- \(B \, t\) is called the linear term
- \(C\) is called the constant term
This is officially known as the standard form.
These are our official library forms.
These are CAN questions.
If a formula CAN be written like \(A \, t + B\), then the function is linear.
If a formula CAN be written like \(A \, t^2 + B \, t + C\), then the function is quadratic.
\(3(x-2) + 9\) is equivalent to \(3x + 3\), so it is linear.
\(\pi (7 - 5x) + 8x\) is equivalent to \((-5\pi + 8) x + 7\pi \), so it is linear.
\(\frac {3+7x}{5}+2x\) is equivalent to \(\frac {17}{5} x + \frac {3}{5}\), so it is linear.
\(3(x-2)^2 + 9\) is equivalent to \(3 x^2 - 12 x + 21\), so it is quadratic.
\(2(x-1)(x+5)\) is equivalent to \(2 x^2 + 8 x - 10\), so it is quadratic.
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more examples can be found by following this link
More Examples of Function Behavior