$\bf \begin{array}{|c|ll} \cline{1-1} slope-intercept~form\\ \cline{1-1} \\ y=\underset{y-intercept}{\stackrel{slope\qquad }{\stackrel{\downarrow }{m}x+\underset{\uparrow }{b}}} \\\\ \cline{1-1} \end{array}~\hspace{6em}\underset{y-intercept}{\stackrel{slope}{y=\stackrel{\downarrow }{4}x\underset{\uparrow }{-5}}}\qquad \qquad \begin{cases} slope\\ \qquad 4\\ y-intercept\\ \qquad (0,-5) \end{cases}$

6 0

4 years ago

Part 1.] Does the graph have even symmetry, odd symmetry, or neither?

QveST [7]

Part 1
The graph has even symmetry. You can see that because it is symmetric with respect to the y-axis.
Functions that have even symmetry have the following property:
$f(x)=f(-x)$
Part 2
To answer this we can simply check if the property we mentioned earlier holds for this function.
$sin(\frac{\pi}{2})\ne sin(-\frac{\pi}{2})$
We can see that sine does not have even symmetry.
In fact, sine function has the following property:
$sin(x)=-sin(x)$
This is called odd symetry.
Part 3
Take a look at the function that you attached in the picture. We know that function has even symmetry.
Reflection over x-axis and 180° rotation around the origin would give us -f(x). We would not end up with the same function, so these two are out.
90° rotation around the origin would mean we swapped x and y so that one is out too. Reflection over the line y=x is a property of functions that have an odd symmetry.
We are left with reflection around y-axis and, as mentioned before, this is the property of evenly symmetric functions.

4 0

4 years ago