Algebra Know-It-ALL
- Imagine an ordered pair (x,y), and suppose we have plotted its point on the Cartesian
plane. Where, in relation to the point for (x,y), will we find the point for (6x, 6y)?
Where, in relation to the point for (x,y), will we find the point for (x/4,y/4)?
- The vertical-line test can be used to see whether or not a graph portrays a function.
How can we use the same test on a graph to determine whether or not a given
numerical value is in the domain?
- How can we use the horizontal-line test on a graph to determine whether or not a given
numerical value is in the range of a function or relation?
- Sketch a graph of the equation y= |x| for all real numbers x. Does this equation
represent a function of x?
- Sketch a graph of the equation y= |x+ 1| for all real numbers x. Does this equation
represent a function of x?
- Sketch a graph of the inverse of y=x+ 1. Do this by applying the “point reflector”
scheme to Fig. 14-11.
- Sketch a graph of the inverse of w=v^2. Do this by applying the “point reflector”
scheme to Fig. 14-12.
- Sketch a graph of the inverse of u=t^3. Don’t use the “point reflector” scheme from
Fig. 14-13. Derive the inverse using algebra, and then plot the graph from scratch.
Practice Exercises 235
