Question

Graph the function. Thanks?!

Answer 1

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

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

Explanation:

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.

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

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`.

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

Answer 2

See below.

Explanation:

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`