Limits questions calculus

Question

Use the graph of the given function f to determine lim x→a f(x)

 at the indicated value of a, if it exists. (If an answer does not exist, enter DNE.)

The x y-coordinate plane is given. A function with 3 parts is graphed. 

1. The first part is linear, enters the window at x = −5 on the negative x-axis, goes up and right, and ends at the open point (−3, 3).
2. The second part is the closed point (−3, 2).
3. The third part is linear, begins at the open point (−3, 3), goes down and right, crosses the y-axis at y = 0.75, crosses the x-axis at x = 1, and exits the window in the fourth quadrant. 
4. The equation a = −3 is shown. 
5. A vertical line extends up from the x−axis at x = −3,passes through the point (−3, 2), and ends at the open circle at (−3, 3).

Answer 1

The limit of f(x) as x→a exists if and only if limit from both sides match: f(x) approaches the same number from the left and the right side.

In other words, lim x→a- f(x) = lim x→a+ f(x) = f(a)..

Here, lim x→a- f(x) = 3, because the line y = 3(x + 5) limits to 3. I used point-slope formula.

Also, lim x→a+ f(x) = 3, because the line y = (-3/4)(x - 1) limits to 3.

So, the limit is 3.

The height of the function at a is 2, so the function has a limit but is discontinuous at x = -3.