Graph the function. Thanks?!

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Answer 1 · 2018-02-05T19:22:44

Graph: graph{5x-3 [-8.58, 11.42, -4, 6]}

The limit when $x->5$ is $22$ .

Drawing the graph

Compare it with the slope-intercept form of a straight line

$y=mx+b$

.![https://www.zazzle.com/y_mx_b_poster-228499487535729869](useruploads.socratic.org)

Here $m$ is the slope $(dy/dx)$ and $b$ is the $y$ -intercept.

enter image source here

Given equation

$y=5x-3$

Slope $(m) = 5$

$y$ -intercept $(b)$ = -3#

Make $y=0$ to get the $x$ -intercept

$0=5x-3 => x=3/5$

We get a graph that looks something like this

enter image source here

Evaluating the limit at $x=5$ $->$ Using the graph

We can see that the graph has no discontinuity/a jump at $x=5$ , thus

$"left-hand limit = right-hand limit = the value of function"("at x = 5")$

Put in $x=5$ and we get $y=22$ .

enter image source here

The limit when $x->5$ is $22$ .

Answer 2 · 2018-02-05T19:33:03

See below.

enter image source here

You can see from the graph that as we approach 5 from the left and from the right that they both limit to 22.

$:.$

$lim_(x->5)(5x-3)=22$

We could have obtained this by plugging in $x=5$ into:

$5x-3$

$5(5)-3=22$

This is a continuous function so the limit exist for every point in the domain, which is $RR$