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Which 3 functions DO NOT have all Real #’s as their domain?

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Which 3 Which 3 functions DO functions DO NOT have all NOT have all Real #’s as Real #’s as their domain? their domain?
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Page 1: Which 3 functions DO NOT have all Real #’s as their domain?

Which 3 functions Which 3 functions DO NOT have all DO NOT have all Real #’s as their Real #’s as their

domain?domain?

Page 2: Which 3 functions DO NOT have all Real #’s as their domain?

Which 3 functions Which 3 functions DO NOT have the DO NOT have the Real #’s as their Real #’s as their

domain?domain?The Reciprocal FunctionThe Reciprocal Function

The Natural Logarithm FunctionThe Natural Logarithm FunctionThe Square Root FunctionThe Square Root Function

Page 3: Which 3 functions DO NOT have all Real #’s as their domain?

Which function has Which function has its domain as the set its domain as the set of all real numbers of all real numbers

except for 0?except for 0?

Page 4: Which 3 functions DO NOT have all Real #’s as their domain?

Which function has Which function has its domain as the set its domain as the set of all real numbers of all real numbers

except for 0?except for 0?The Reciprocal FunctionThe Reciprocal Function

Page 5: Which 3 functions DO NOT have all Real #’s as their domain?

Which 2 functions Which 2 functions have no negative #’s in have no negative #’s in

their domain?their domain?

Page 6: Which 3 functions DO NOT have all Real #’s as their domain?

Which 2 functions Which 2 functions have no negative #’s in have no negative #’s in

their domain?their domain?

The Square Root FunctionThe Square Root Function The Natural Logarithm The Natural Logarithm

FunctionFunction

Page 7: Which 3 functions DO NOT have all Real #’s as their domain?

Which function(s) have Which function(s) have some type of discontinuity? some type of discontinuity?

Be prepared to tell what Be prepared to tell what type of discontinuity it is.type of discontinuity it is.

Page 8: Which 3 functions DO NOT have all Real #’s as their domain?

Which 2 functions have Which 2 functions have some type of discontinuity? some type of discontinuity?

Be prepared to tell what Be prepared to tell what type of discontinuity it is.type of discontinuity it is. The Reciprocal function (infinite)The Reciprocal function (infinite)

It is an infinite discontinuityIt is an infinite discontinuity

Page 9: Which 3 functions DO NOT have all Real #’s as their domain?

Only 3 of the functions Only 3 of the functions are bounded both are bounded both above and below. above and below.

Which three?Which three?

Page 10: Which 3 functions DO NOT have all Real #’s as their domain?

Only 3 of the functions Only 3 of the functions are bounded both are bounded both above and below. above and below.

Which three?Which three? The Sine FunctionThe Sine Function

The Cosine FunctionThe Cosine Function The Logistic FunctionThe Logistic Function

Page 11: Which 3 functions DO NOT have all Real #’s as their domain?

Three of the 11 Three of the 11 basic functions are basic functions are

EVEN.EVEN.Which are they?Which are they?

Page 12: Which 3 functions DO NOT have all Real #’s as their domain?

Three of 11 basic Three of 11 basic functions are EVEN.functions are EVEN.

Which are they?Which are they?

•The Cosine Function

•The Absolute Value Function

•The Squaring Function

Page 13: Which 3 functions DO NOT have all Real #’s as their domain?

Two of the eleven basic Two of the eleven basic functions have vertical functions have vertical

asymptotes at x=0.asymptotes at x=0.Which are they?Which are they?

Page 14: Which 3 functions DO NOT have all Real #’s as their domain?

Two of the eleven basic Two of the eleven basic functions have vertical functions have vertical

asymptotes at x=0.asymptotes at x=0.Which are they?Which are they?

The Reciprocal FunctionThe Reciprocal Function The Natural Logarithm FunctionThe Natural Logarithm Function

Page 15: Which 3 functions DO NOT have all Real #’s as their domain?

Three of the elevenThree of the elevenbasic functions have basic functions have

horizontal asymptotes horizontal asymptotes at y=0. Which three?at y=0. Which three?

Page 16: Which 3 functions DO NOT have all Real #’s as their domain?

Three of the eleven Three of the eleven basic functions have basic functions have

horizontal asymptotes horizontal asymptotes at y=0. Which two?at y=0. Which two?

The Exponential FunctionThe Exponential Function The Logistic FunctionThe Logistic Function

The Reciprocal FunctionThe Reciprocal Function

Page 17: Which 3 functions DO NOT have all Real #’s as their domain?

Which four basic Which four basic functions are functions are

ODD?ODD?

Page 18: Which 3 functions DO NOT have all Real #’s as their domain?

Which four basic Which four basic functions are functions are

ODD?ODD? The Cubing FunctionThe Cubing Function

The Sine FunctionThe Sine Function The Reciprocal FunctionThe Reciprocal Function

The Identity FunctionThe Identity Function

Page 19: Which 3 functions DO NOT have all Real #’s as their domain?

Which 6 functions Which 6 functions increase on their increase on their entire domain?entire domain?

Page 20: Which 3 functions DO NOT have all Real #’s as their domain?

Which 6 functions Which 6 functions increase on their increase on their entire domain?entire domain?

The Identity FunctionThe Identity Function The Natural Logarithm FunctionThe Natural Logarithm Function

The Cubing FunctionThe Cubing Function The Exponential FunctionThe Exponential Function The Square Root Function The Square Root Function

The Logistic FunctionThe Logistic Function

Page 21: Which 3 functions DO NOT have all Real #’s as their domain?

Which 3 functions are Which 3 functions are decreasing on the decreasing on the interval ?interval ? ,0

Page 22: Which 3 functions DO NOT have all Real #’s as their domain?

Which 3 functions are Which 3 functions are decreasing on the decreasing on the interval ?interval ?

The Absolute Value FunctionThe Absolute Value Function The Reciprocal FunctionThe Reciprocal Function The Squaring FunctionThe Squaring Function

,0

Page 23: Which 3 functions DO NOT have all Real #’s as their domain?

Which three Which three functions functions

have NO zeros?have NO zeros?

Page 24: Which 3 functions DO NOT have all Real #’s as their domain?

Which three Which three functions functions

have NO zeros?have NO zeros? The Reciprocal FunctionThe Reciprocal Function

The Exponential FunctionThe Exponential Function The Logisitic FunctionThe Logisitic Function

Page 25: Which 3 functions DO NOT have all Real #’s as their domain?

Which 3 functions Which 3 functions have a range of have a range of

? ?

,

Page 26: Which 3 functions DO NOT have all Real #’s as their domain?

Which 3 functions Which 3 functions have a range of have a range of

?? The Identity FunctionThe Identity Function

The Natural Logarithm FunctionThe Natural Logarithm Function The Cubing FunctionThe Cubing Function

,

Page 27: Which 3 functions DO NOT have all Real #’s as their domain?

Which 2 functions Which 2 functions have graphs that are have graphs that are identical except for a identical except for a

horizontal shift?horizontal shift?

Page 28: Which 3 functions DO NOT have all Real #’s as their domain?

Which 2 functions Which 2 functions have graphs that are have graphs that are Identical except for a Identical except for a

horizontal shift?horizontal shift? The Cosine FunctionThe Cosine Function

The Sine FunctionThe Sine Function


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