Chapter 2 - Section 2.6 - Function Notation and Linear Functions - 2.6 Exercises: 58

$\text{Domain: } (-\infty,\infty) \\\text{Range: } (-\infty,\infty)$

Work Step by Step

$\bf{\text{Solution Outline:}}$ To graph the given linear function, $H(x)=-3x ,$ find two points on the line by identifying the $y$-intercept and the slope. Use the geometric interpretation of slope as $\dfrac{rise}{run}.$ Then use the graph to identify the domain and range of the function. $\bf{\text{Solution Details:}}$ A linear function in the form $f(x)=mx+b,$ has a $y$-intercept of $b$ and a slope of $m.$ Since the $y$-intercept is $0 ,$ the graph passes through $(0, 0 ).$ With a slope of $m= -3=\dfrac{-3}{1} =\dfrac{rise}{run} ,$ then from the $y$-intercept, move $3$ units down and then $1$ unit to the right to get the point $( 1,-3 ).$ Based on the graph the domain and range are as follows: \begin{array}{l}\require{cancel} \text{Domain: } (-\infty,\infty) \\\text{Range: } (-\infty,\infty) .\end{array}

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