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#

.

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#