Counterexamples and Logic Symbols HW
1 answer:
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Given:
The function is:
To find:
a. Slope and Y-intercept.
b. Is the function increasing, decreasing, or constant, justify your answer.
c. Graph the function, label x, and y-intercepts.
Solution:
a. We have,
...(i)
The slope intercept form of a line is:
...(ii)
Where, m is the slope and b is the y-intercept.
On comparing (i) and (ii), we get
Therefore, the slope of the line is -2 and the y-intercept is 1.
b. If the slope of a linear function is negative, then the function is decreasing.
If the slope of a linear function is positive, then the function is increasing.
If the slope of a linear function is 0, then the function is constant.
The slope of the linear function is negative.
Therefore, the function is decreasing.
c. We have,
At , we get
So, the y-intercept is at (0,1).
At , we get
So, the x-intercept is at .
Plot the points and connect them by a straight line as shown below:
