Question

Can someone answer this?

Answer 1

Answer:

$\lim_{x\to 3^-} f(x)=-1$

Step-by-step explanation:

We have a piesewise function composed of three pieces. two line segments and one point.

The first line cuts at point (0,0) and ends at point (3, -1)

If we use these two points we can find the equation of the line.

The slope m is:

$m = \frac{y_2-y_1}{x_2-x_1}\\\\m = \frac{-1 - (0)}{3-0}\\\\m = -\frac{1}{3}$

So the equation is:

$y = -\frac{1}{3}x + b$

As the line cuts in (0,0) then $b = 0$ and the equation is:

$y = -\frac{1}{3}x$

The equation of the second line is:

$y = -4$

Now we can find f(x) (although it is not necessary to find the equation of f(x) because we have its graph)

$f(x) = -\frac{1}{3}x$   if  $x$;  $f(x)=-4$   if   $x> 3$;   $f(x)= 7$   if   $x = 3$.

The limit of f(x) when x tends to 3 from the left  $\lim_{x\to 3^-} f(x)$ is the limit of the function  when x approaches 3 from the left. If x approaches 3 from the left then $x$. If $x$ then f(x) is given by the line $y = -\frac{1}{3}x$ . Then the limit is -1  as seen in the graph