Section 1.1 : Review : Functions
5. The difference quotient of a function \(f\left( x \right)\) is defined to be,
\[\frac{{f\left( {x + h} \right) - f\left( x \right)}}{h}\]compute the difference quotient for \(f\left( x \right) = 4x - 9\).
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Hint : Compute \(f\left( {x + h} \right)\), then compute the numerator and finally compute the difference quotient.
\[f\left( {x + h} \right) = 4\left( {x + h} \right) - 9 = 4x + 4h - 9\]
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\[f\left( {x + h} \right) - f\left( x \right) = 4x + 4h - 9 - \left( {4x - 9} \right) = 4h\]
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\[\frac{{f\left( {x + h} \right) - f\left( x \right)}}{h} = \frac{{4h}}{h} = 4\]