graph for y = / x + 4 / ?

Question

struggling badly in online precal class, need help with graphs of functions, etc

Answer 1

Absolute value functions will never go below the x axis (because there's no such thing as a negative absolute value).  If you were graphing the absolute value of any function, when it would normally go beneath the x axis, and would have negative values of y, you just change those values to positive values, "flipping" the graph over the x axis. 

Probably the easiest example of this is y = |x|.  y = x, is just a straight line, slope equals one, passing through the origin (0,0).  Once it passes through the origin, where it would be negative (in the bottom left quadrant) the absolute value function is made positive and the resulting graph looks like a V.  Any linear function (like the one you have) is going to look like a V, though the steepness of the slope and location of the sharp point of the V depend on the function.

In your case, the V has a slope of -1 on the left side and 1 on the right.  The sharp point (where the slope changes) is located at (-4,0), the point where the function intersects the x axis.

Answer 2

Given the equation y = |x + 4|, we know one thing to begin with. The absolute value of any number can never be less than 0. This means that for this equation, y must always be 0 or greater. Knowing this helps you to know what to expect when the graph is drawn.

Y is positive, but we don't know if x + 4 is positive or negative before taking the absolute value. To account for both possibilities, we need to take the original equation and write two possible resulting equations:

Y = (x + 4)

or

Y = -(x + 4)

Solving the first: y = x + 4 will be true as long as x + 4 is greater than or equal to 0.

Solving the second y = -(x + 4) becomes y = -x - 4, which will be true when x + 4 is less than 0.