Practice Exercises in Software

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This is an open-book quiz You may (and should) refer to the text as you solve these problems Don t hurry! You ll find worked-out answers in App B The solutions in the appendix may not represent the only way a problem can be figured out If you think you can solve a particular problem in a quicker or better way than you see there, by all means try it! 1 Imagine an ordered pair (x, y), and suppose we have plotted its point on the Cartesian plane Neither x nor y is equal to 0, so the point does not fall on either axis What happens to the location of the point if we multiply x by 1 and leave y the same 2 Imagine an ordered pair (x, y), and suppose we have plotted its point on the Cartesian plane Neither x nor y is equal to 0, so the point does not fall on either axis What happens to the location of the point if we multiply y by 1 and leave x the same

3 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) 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 5 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 6 Sketch a graph of the equation y = |x | for all real numbers x Does this equation represent a function of x 7 Sketch a graph of the equation y = |x + 1| for all real numbers x Does this equation represent a function of x 8 Sketch a graph of the inverse of y = x + 1 Do this by applying the point reflector scheme to Fig 14-11 9 Sketch a graph of the inverse of w = v 2 Do this by applying the point reflector scheme to Fig 14-12 10 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

We ve seen the graphs of some relations and functions Now it s time to focus on the graphs of linear relations These always appear as straight lines in the Cartesian plane In particular, we re interested in the equations and graphs of linear functions linear relations where the straightline graph is not vertical (that is, not parallel to the dependent-variable axis)

One of the best known ways to relate the graph of a linear function with its equation defines the slope of the line and the point where it crosses the dependent-variable axis A two-variable linear equation of this sort is said to be in slope-intercept form Let s call it the SI form for short

What is slope The slope of a straight line in the Cartesian plane is an expression of the steepness with which the line ramps upward or downward as we move to the right A horizontal line has a slope of 0 A line that ramps upward as we move to the right has positive slope that increases without limit as the slant angle approaches 90 (vertical and going straight up) If the line ramps down as we move to the right, the slope decreases from 0, becoming more negative without limit as the slant angle approaches 90 (vertical and going straight down) To figure out the exact slope of a line in the Cartesian plane, we must know the coordinates of two points on that line These can be any two points, as long as they re different The slope of a line passing through two points is equal to the difference in the y values divided by the difference in the x values for the points In this context, mathematicians abbreviate the difference in by writing the uppercase Greek letter delta ( ) These differences are often called increments The slope of a line is usually symbolized as m Therefore,