## Intermediate Algebra (12th Edition)

$\text{Domain: } (-\infty,\infty) \\\text{Range: } (-\infty,\infty)$
$\bf{\text{Solution Outline:}}$ To graph the given linear function, $F(x)=-\dfrac{1}{4}x+1 ,$ 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 $1 ,$ the graph passes through $(0, 1 ).$ With a slope of $m= -\dfrac{1}{4}=\dfrac{-1}{4} =\dfrac{rise}{run} ,$ then from the $y$-intercept, move $1$ unit down and then $4$ units to the right to get the point $( 4,0 ).$ 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}