The 12 Basic Functions

How many of the twelve basic functions look the same when flipped about the y-axis? List them.

2; The absolute value and squaring functions

How many of the twelve basic functions are even? List them.

3; The absolute value, squaring, and cosine functions

How many of the twelve basic functions have end behavior lim f(x)=-∞, x--->-∞? List them.

3; The identity, cubing, and greatest integer functions

How many of the twelve basic functions have a range of all real numbers?

3; The identity, cubing, and natural logarithm functions

How many of the twelve basic functions look the same upside down as right-side up? List them.

None

Which functions are bounded above?

None

Which functions are bounded below?

The absolute value, exponential, square root, and squaring functions

Which functions are not bounded?

The greatest integer, natural logarithm, cubing, reciprocal, and identity functions

Identify the six basic functions that are increasing on their entire domains.

The identity, cubing, exponential, natural logarithm, square root, and logistic functions

Identify the four basic functions that are odd.

The identity, cubing, reciprocal, and sine functions

Which functions are bounded above and below?

The logistic, cosine, and sine functions

Identify the four functions that do NOT have end behavior lim f(x)=∞, x--->∞

The logistic, reciprocal, sine, and cosine functions

Which of the twelve basic functions are not continuous?

The reciprocal (infinite discontinuity) and greatest integer (jump discontinuity) functions

Which ones are decreasing on their entire domain?

The reciprocal function only

Identify the three basic functions with no zeros

The reciprocal, exponential, and logistics functions

Seven of the twelve basic functions have the property that f(0)=0. Which five do not?

The reciprocal, exponential, natural logarithm, cosine, and logistic functions

Which ones do not have a domain of all real numbers?

The reciprocal, square root, and natural logarithm functions

Identify the three basic functions that are decreasing on the interval (-∞,0)

The squaring, absolute value, and reciprocal functions