A. What is similarities and differences do you see between functions and linear equations studied in Ch. 3?
Functions and linear equations have elements which create straight lines when plotted on the graph. Both linear equation and a function are polynomial to the first degree. A linear equation and function have variables that are paired and separated by comma in a bracket. The variables are normally in form of x and y with each having one value. A linear equation is an algebraic expression having two variables with similar value while a function has only one variable. The major use of a function is to in key and out key number while linear equation is use to ascertain the gradient and position of a line. Linear equations are found in the form y=mx+b while functions can be found in more various forms including be put in to T-chart.
B. Are all linear equations functions?
Functions and linear equations are similar; however, not all linear equations are functions. They both uses the variables x and y coordinates but for different purposes. Linear equations require you to solve the question whereas function already has its values that are inserted in the equation to get the answer. In finding the solution of a function the slope, y-intercept and two graphical points are mandatory. However, the vertical line in any plot does not present a function.
C. Is there an instance in which a linear equation is not a function? Support your answer.
All linear equations are not functions. A linear equation is not a function when it does not make a straight line, for example when it is a parabola or if it makes a vertical line. Linear equations can be represented on a Cartesian plane to determine whether the predetermined equation is a linear equation or a function. If the x axis intersects at more than one value on the points, then that the linear equation is not a function. A vertical line is not a function because it has only one value in the y-intercept. Functions must have both the values for y and x. A function can either be a linear or non-linear. Linear lines presented graphically produce a straight line and this makes it a function. Functions produce the values of either x or y while a linear equation, the solution of both x and y are computed. A nonlinear function would y= x2 becomes a parabola when graphed. More examples of nonlinear functions:
y = x2 + 6
y= x2+ 5x + 10
y = 6x2
D. All linear equations are not always functions.
A linear equation is not a function when it does not make a straight line. The similarity between the two is that they share x and y variables. Functions depict the unique correspondence between the domain and the range. Graphing linear equations need a plot two points and a third to check it with the slope while a function requires a specific number that represents the domain and the corresponding range.
E. Linear equation:
1. Find the slope of point (2,5) and (3,6)
m = 1
Find the slope, y-intercept and two graphical points
y=2x + 3
the slope is 2
at y-intercept x = 0
two graphical points are:
y = 2x + 3
5 = 2x + 3
F. Can a linear equation to be graphed as a vertical line a function. Why or why not?
Linear equation cannot be graphed as a vertical line function. This because when it comes to graphing linear equations there is also the need to plot two points and a third to check it with the slope. Linear equation always take the form of straight lines with two variables of x and y respectively.
Discussion Question 2
What is the difference between domain and range?
Domain of a function is a set of all values of x while range of is the set all values that the function takes when x takes the values of the domain. It can take either positive values, negative values or zero.
Describe a real life situation that could be modeled by a function.
A function could, for instance, designate the quantity of bone muscle (y) in a existing individual above instant in days (x).
Describe the values for x that may not be appropriate values even when they are defined of your classmates’ function
It is insensible to glance at negative years. This is because the person would not have existeted. Similarly, viewing beyond 100 years is unrealistic, since most people do not stay up to 100 years.
G. The different between the domain and the range
Domain is an autonomous function since it takes the values of the variable x while the range is a reliant variable since it takes the values of variable y. The variable values of the range normally rely on the domain. X values of function are input, where the function is logically defined while Y values the result of out puts over sensibly.
H. There is a set of possible for the variables of (x). Do you think that if all set points are not made the problem will come out wrong? All numbers do have function if they are set in the right order. Do you agree?
The distance in time when driving a vehicle is different from walking because of the different in speed. The farthest you drive the longer time you take. Therefore, the placing and timing need to be correct in order to get all parts of the problem correct.