# Graph the function. Thanks?!

## Feb 5, 2018

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

The limit when $x \to 5$ is $22$.

#### Explanation:

Drawing the graph

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

$y = m x + b$

. Here $m$ is the slope $\left(\frac{\mathrm{dy}}{\mathrm{dx}}\right)$ and $b$ is the $y$-intercept. Given equation

$y = 5 x - 3$

• Slope $\left(m\right) = 5$
• $y$-intercept $\left(b\right)$ = -3

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

$0 = 5 x - 3 \implies x = \frac{3}{5}$

We get a graph that looks something like this Evaluating the limit at $x = 5$ $\to$ 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 $x \to 5$ is $22$.

Feb 5, 2018

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.

$\therefore$

${\lim}_{x \to 5} \left(5 x - 3\right) = 22$

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

$5 x - 3$

$5 \left(5\right) - 3 = 22$

This is a continuous function so the limit exist for every point in the domain, which is $\mathbb{R}$