## (Section 8)

##### I.
 Function is positive (y>0) when x >0 y is positive when x is positive Function is negative (y<0) when x<0 y is negative when x is negative Function equal to zero when x = 0 y is zero when x is zero Slope of function constant (always equal to 1) slope is constant--always 1
##### II.  or

 Function is positive (y>0) when x >0 or  x <0 y values are positive for any value of x no equal to zero. Function equal to zero when x = 0 y equals 0 only when x equals zero Slope of function constant when x <0 (always equal to -1) and constant when x>0 (always equal to +1) two different slopes

##### III.
 Function is positive (y>0) when x >0 or x<0 y is positive when x is negative Function equal to zero when x = 0 y equals zero when x equals zero Slope is negative and changing when x<0 slope is negative and changing when x is negative--  As x values increase, the slope increases Slope is zero when x = 0 slope is zero when x is zero Slope is positive and changing when x>0 slope is positive and changing when x is positive--  As x increases the slope increases

##### IV.
 Function is positive (y>0) when x >0 y is positive when x is positive Function is negative (y<0) when x<0 y is negative when x is negative Function equal to zero when x = 0 y is zero when x is zero Slope is always positive when x is not equal to zero slope is positive and changing when x is negative--As x increases the slope increases  slope is positive and changing when x is positive--As x increases the slope increases Slope is zero when x = 0 slope is zero when x is zero

##### V.
 Function is positive (y>0) when x >0 y is positive when x is positive y values are increasing as x values increase Function is negative (y<0) when x<0 y is negative when x is negative y values are increasing as x values increase Function equal to zero when x = 0 y is zero when x is zero Slope is always positive when x is not equal to zero slope is positive and increasing as x values are negative and increasing slope is positive and decreasing when x is positive and increasing Slope is undefined when x = 0 slope is undefined at (0,0) or you can draw a tangent line with no slope at the point (0,0)

##### VI.
 Function is positive (y>0) when x >0 y is positive when x is positive Function is negative (y<0) when x<0 y is negative when x is negative Function is not defined when x = 0 y is undefined when x is zero Slope is negative and changing when x does not equal zero slope is negative and decreasing as x is negative and increasing slope is negative and increasing when x is positive and increasing

##### VII.
 This equation is not a function of x or y but can be written as two functions or is positive for all values of x between -2 and 2 inclusive y is positive for all x between -2 and 2 inclusive is negative for all values of x between -2 and 2 inclusive y is negative for all x between -2 and 2 inclusive has positive slope when x>-2 and x<0 slope is positive and decreasing as x goes from -2 to 0 has negative slope when x>-2 and x<0 slope is negative and increasing as x goes from -2 to 0 has zero slope when x = 0 slope is zero when x is zero has zero slope when x = 0 slope is zero when x is zero has negative slope when x>0 and x<2 slope is negative and decreasing as x goes from 0 to 2 has positive slope when x>0 and x<2 slope is positive and increasing as x goes from 0 to 2 has undefined slope when x = -2 or x = 2 Slope is undefined when x is -2 or 2 has undefined slope when x = -2 or x = 2 slope is undefined when x is -2 or 2
##### VIII.
 is positive for all values of x between -2 and 2 inclusive y is positive when x is between -2 and 2 is zero for x = -2 and x = +2 y is zero when x equals -2 and -2 has positive slope when x>-2 and x<0 slope is positive and decreasing as x changes from -2 to 0 has zero slope when x = 0 slope is zero when x = 0 has negative slope when x>0 and x<2 slope is negative and decreasing as x changes from 0 to 2 has undefined slope when x = -2 or x = 2 slope is undefined at x equals -2 and 2
##### IX.
 This equation is not a function of x or y but can be written as two functions or is positive for all values of x between -2 and 2 inclusive y is positive when x is between -2 and 2 is negative for all values of x between -2 and 2 inclusive y is negative when x is between -2 and 2 has positive slope when x>-2 and x<0 slope is positive and decreasing as x increases from -2 to 0 has negative slope when x>-2 and x<0 slope is negative and increasing as x increases from -2 to 0 has zero slope when x = 0 slope is zero when x = 0 has zero slope when x = 0 slope is zero when x is zero has negative slope when x>0 and x<2 slope is negative and decreasing as x increases from 0 to 2 has positive slope when x>0 and x<2 slope is positive and increasing as x increases from 0 to 2 has undefined slope when x = -2 or x = 2 slope is undefined at x equals -2 and +2 has undefined slope when x = -2 or x = 2 slope is undefined at x equals -2 and +2

##### X.
 This equation is not a function of x or y but can be written as two functions or is positive for all values of x less than -2 or all x values greater than 2 y is positive when x is greater than 2 or x is less than -2. is negative for all values of x between -2 and 2 inclusive y is negative when x is greater than 2 or x is less than -2 has negative slope when x<-2 slope is negative and decreasing as x increases from negative infinity to -2 has positive slope when x<-2 slope is positive and increasing as x increase from negative infinity to -2 has positive slope when x>2 slope is positive and decreasing as x increases from 2 to infinity has negative slope when x>2 slope is native and increases as x increases from 2 to infinity has undefined slope when x = -2 or x = 2 slope is undefined at x equal -2 or 2 has undefined slope when x = -2 or x = 2 slope is undefined at x equal -2 or 2

##### XI.
 is positive for all values of x y is positive for all x values has positive slope for all values of x slope is positive and increasing as x increases-- slope approaches zero as x approaches negative infinity never equals zero for any values of x y is never zero or negative

##### XII.
 is positive for all values of x>1 y is positive when x is greater than 1 is negative for all values of x>0 and X<1 y is negative when x is less than 1 is equal to zero for x=1 y is zero when x is 1 is positive slope for any values of x>0 slope is positive for all x slope is approaching zero as x approaches positive infinity