Properties of Functions?

Question

Using these functions:

Absolute value, constant, cubic, exponential, linear, logarithmic, quadratic, radical, rational, and step

What is the physical shape? does it cross the x or y axis? critical turning points? final destination?

Answer 1

Absolute value. I guess that means f(x) = abs(x)
This looks like a "V" with the vertex at (0,0). Therefore it DOES cross the Y axis, but it only touches, but does not cross, the x axis. There is no "final destination" because if you increase x without limit, y keeps increasing as well.

Constant means f(x) = k where K can be any number. Draw it on a graph and see for yourself that it crosses the Y axis, but not the x axis. It might be ON the x axis, but it doesn't cross. It has no turning points, and its final destination is K

You can do the rest in the same manner. Pay special attention to the logarithmic and radial functions, because they do NOT cross the y axis. That is, you are NOT allowed zero or negative numbers in a log function, and you are allowed zero but no negative numbers in a radical!