Writing Prompt #2
Inverses
Three of the following statements below are false. First determine if each statement is true or false. If If a
statement is false, give an example with supporting verbal evidence that shows why it is false. Graphs may be
used to enhance your verbal response.
f
1.
If
is an even function than
2.
If the inverse of
3.
If
4.
There exists no function
f ( x ) = xn
f
f −1
exists.
exists, the y-intercept of
where n is odd,
f
f
is an x-intercept of
f −1 .
f −1 exists.
such that
f
=
f −1 .
#1 this is false,
false, for example f(x) = x2 is an even function and it looks like
so when you look at the
inverse for this function it would not be a function (it fails the horizontal line test.) This also means it is
not a oneone-toto-one function.
#2 this is true To find an inverse, we interchange the x and yy-coordinates of a point. Therefore, if
a graph has a y - intercept of (0, 6) for example, and the x and y - coordinates are interchanged, the
resulting coordinate is (6, 0) . Since the value of y is zero in the new coordinate, it lies on the x - axis and is
therefore an x - intercept of the inverse function.
#3 this is true We can test this function to determine if it is even, odd or neither by evaluating f ( −x ) .
This means that we need to plug in −x to the equation and evaluate the function. Since n is odd in the
function f (x ) = x n , then f ( −x ) = −x n because raising a negative number to an odd power will always result in
a negative base. Therefore, if the function is odd, it has origin symmetry and will pass both the vertical and
horizontal line test, making it one - to - one. If the function is one - to - one, then it has an inverse.
()
#4 this is false,
false, for example one function we looked at in class is f x =
()
f −1 x =
1
x
. The graph for this function looks like.
1
x
whose inverse is also
Writing Prompt #3
Point-Slope Form vs. Slope-intercept
Describe and provide examples of when it is easier to use the point-slope form to write the equation of a line and
when it is easier to use the slope-intercept form. Also indicate when neither of these forms is an appropriate
equation of a line.
If you are given the point and a slope, the easiest form to write an equation of a line is point-slope.
You have all of the information you need to create the line. For example, (2, -3) and m = -5... the equation
is:
y+3 = -5(x-2).
However, if you have the y-intercept and a slope the easier form to use would be slope-intercept. For
example, if the slope is 17 and you are given the y-intercept of -12, the equation of the line would be
y = 17x - 12.
Finally, if you need to write the equation of a vertical line, you can't use either of these forms. You
will need to write x = and the x-intercept of the line. For example, if you have a vertical line going through the
point (-8,4), the equation would be x= -8.